
-
Previous Article
A fractional model for the dynamics of tuberculosis (TB) using Atangana-Baleanu derivative
- DCDS-S Home
- This Issue
-
Next Article
Existence results of Hilfer integro-differential equations with fractional order
Optical solitons to the fractional perturbed NLSE in nano-fibers
1. | Firat University, Faculty of Science, 23119 Elazig, Turkey |
2. | Federal University Dutse, Faculty of Science, 7156 Jigawa, Nigeria |
3. | Final International University, Faculty of Education, Kyrenia, Cyprus |
4. | Harran University, Faculty of Education, 63290 Sanliurfa, Turkey |
In this paper, we study the space-time fractional perturbed nonlinear Schr$ \bf{\ddot o} $dinger equation under the Kerr law nonlinearity by using the extended sinh-Gordon equation expansion method. The perturbed nonlinear Schr$ \bf{\ddot o} $dinger equation is a nonlinear model which arises in nano-fibers. Some family of optical solitons and singular periodic wave solutions are successfully revealed. The parametric conditions for the existence of valid solitons are stated. Under the choice of suitable values of the parameters, the 3-dimensional and 2-dimensional graphs to some of the reported solutions are plotted.
References:
[1] |
A. Abdon and B. Dumitru, New fractional derivatives with nonlocal and non-singular kernel: Theory and application to heat transfer model, Thermal Science, 20 (2016), 763-769. Google Scholar |
[2] |
M. A. Akinlar and M. Kurulay, A novel method for analytical solutions of fractional partial differential equations, Mathematical Problems in Engineering, 2013 (2013), Art. ID 195708, 4 pp.
doi: 10.1155/2013/195708. |
[3] |
K. K. Ali, R. I. Nuruddeen and K. R. Raslan,
New structures for the space-time fractional simplified MCH and SRLW equations, Chaos, Solitons and Fractals, 106 (2018), 304-309.
doi: 10.1016/j.chaos.2017.11.038. |
[4] |
S. Arbabi and M. Najafi, Exact solitary wave solutions of the complex nonlinear Schr$ \bf{\ddot o}$dinger equations, Optik, 127 (2016), 4682-4688. Google Scholar |
[5] |
A. H. Arnous, M. Z. Ullah, M. Asma, S. P. Moshokoa, Q. Zhou, M. Mirzazadeh, A. Biswas and M. Belic, Dark and singular dispersive optical solitons of Schr$ \bf{\ddot o}$dinger-Hirota equation by modified simple equation method, Optik, 136 (2017), 445-450. Google Scholar |
[6] |
M. Arshad, A. R. Seadawy and D. Lu, Elliptic function and solitary wave solutions of the higher-order nonlinear Schr$ \bf{\ddot o}$dinger dynamical equation with fourth-order dispersion and cubic-quintic nonlinearity and its stability, The European Physical Journal Plus, 132 (2017), 371. Google Scholar |
[7] |
A. Atangana and D. Baleanu,
Application of Fixed Point Theorem for Stability Analysis of a Nonlinear Schrodinger with Caputo-Liouville Derivatives, Filomat, 31 (2017), 2243-2248.
doi: 10.2298/FIL1708243A. |
[8] |
E. Bas, R. Yilmaza and E. Panakhov, Fractional solutions of bessel equation with $N$-method, The Scientific World Journal, 2013 (2013), Article ID 685695, 8 pages.
doi: 10.1155/2013/685695. |
[9] |
H. M. Baskonus, T. A. Sulaiman, H. Bulut and T. Akturk, Investigations of dark, bright, combined dark-bright optical and other soliton solutions in the complex cubic nonlinear Schr$ \bf{\ddot o}$dinger equation with $\delta$-potential, Superlattices and Microstructures, 115 (2016), 19-29. Google Scholar |
[10] |
H. M. Baskonus, H. Bulut and T. A. Sulaiman,
Investigation of various travelling wave solutions to the extended (2+1)-dimensional quantum ZK equation, The European Physical Journal Plus, 132 (2017), 482.
doi: 10.1140/epjp/i2017-11778-y. |
[11] |
H. M. Baskonus, T. A. Sulaiman and H. Bulut, Dark, bright and other optical solitons to the decoupled nonlinear Schr$ \bf{\ddot o}$dinger equation arising in dual-core optical fibers, Opt Quant Electron, 50 (2018), 165. Google Scholar |
[12] |
H. M. Baskonus, T. A. Sulaiman and H. Bulut,
Bright, dark optical and other solitons to the generalized higher-order NLSE in optical fibers, Opt Quant Electron, 50 (2018), 253.
doi: 10.1007/s11082-018-1522-0. |
[13] |
I. Bendahmane, H. Triki, A. Biswas, A. S. Alshomrani, Q. Zhou, S. P. Moshokoa and M. Belic, Bright, dark and W-shaped solitons with extended nonlinear Schr$ \bf{\ddot o}$dinger's equation for odd and even higher-order terms, Superlattices Microstruct., 114 (2018), 53-61. Google Scholar |
[14] |
A. H. Bhrawy, A. A. Alshaery, E. M. Hilal, Z. Jovanoski and A. Biswas,
Bright and dark solitons in a cascaded system, Optik, 125 (2014), 6162-6165.
doi: 10.1016/j.ijleo.2014.06.118. |
[15] |
A. Biswas, M. Ekici, A. Sonmezoglu, Q. Zhou, S. P. Moshokoa and M. Belic,
Optical soliton perturbation with full nonlinearity for Kundu-Eckhaus equation by extended trial function scheme, Optik, 160 (2018), 17-23.
doi: 10.1016/j.ijleo.2018.01.111. |
[16] |
A. Biswas, Q. Zhou, S. P. Moshokoa, H. Triki, M. Belic and R. T. Alqahtani,
Resonant 1-soliton solution in anti-cubic nonlinear medium with perturbations, Optik, 145 (2017), 14-17.
doi: 10.1016/j.ijleo.2017.07.036. |
[17] |
A. Biswas, Q. Zhou, M. Z. Ullah, H. Triki, S. P. Moshokoa and M. Belic,
Optical soliton perturbation with anti-cubic nonlinearity by semi-inverse variational principle, Optik, 143 (2017), 131-134.
doi: 10.1016/j.ijleo.2017.06.087. |
[18] |
A. Biswas, A. H. Kara, M. Z. Ullah, Q. Zhou, H. Triki and M. Belic,
Conservation laws for cubic-quartic optical solitons in Kerr and power law media, Optik, 145 (2017), 650-654.
doi: 10.1016/j.ijleo.2017.08.047. |
[19] |
A. Biswas, H. Triki, Q. Zhou, S. P. Moshokoa, M. Z. Ullah and M. Belic,
Cubic-quartic optical solitons in Kerr and power law media, Commun. Theor. Phys., 144 (2017), 357-362.
doi: 10.1016/j.ijleo.2017.07.008. |
[20] |
H. Bulut, T. A. Sulaiman and B. Demirdag, Dynamics of soliton solutions in the chiral nonlinear Schr$ \bf{\ddot o}$dinger equations, Nonlinear Dynamics, 91 (2018), 1985-1991. Google Scholar |
[21] |
H. Bulut, T. A. Sulaiman, H. M. Baskonus and T. Akturk,
Complex acoustic gravity wave behaviors to some mathematical models arising in fluid dynamics and nonlinear dispersive media, Opt Quant Electron, 50 (2018), 19.
doi: 10.1007/s11082-017-1286-y. |
[22] |
H. Bulut, T. A. Sulaiman, H. M. Baskonus, H. Rezazadeh, M. Eslami and M. Mirzazadeh,
Optical solitons and other solutions to the conformable space-time fractional Fokas-Lenells equation, Optik, 127 (2018), 20-27.
doi: 10.1016/j.ijleo.2018.06.108. |
[23] |
H. Bulut, T. A. Sulaiman and H. M. Baskonus,
On the new soliton and optical wave structures to some nonlinear evolution equation, The European Physical Journal Plus, 132 (2017), 459.
doi: 10.1140/epjp/i2017-11738-7. |
[24] |
C. Cattani,
Harmonic wavelet solutions of the Schrodinger equation, International Journal of Fluid Mechanics Research, 30 (2003), 463-472.
doi: 10.1615/InterJFluidMechRes.v30.i5.10. |
[25] |
C. Cattani, T. A. Sulaiman, H. M. Baskonus and H. Bulut,
Solitons in an inhomogeneous Murnaghan's rod, Eur. Phys. J. Plus, 133 (2018), 228.
doi: 10.1140/epjp/i2018-12085-y. |
[26] |
C. Cattani, T. A. Sulaiman, H. M. Baskonus and H. Bulut,
On the soliton solutions to the Nizhnik-Novikov-Veselov and the Drinfel'd-Sokolov systems, Opt Quant Electron, 50 (2018), 138.
doi: 10.1007/s11082-018-1406-3. |
[27] |
M. T. Darvishi, S. Ahmadian, S. B. Arbabi and M. Najafi, Optical solitons for a family of nonlinear (1+1)-dimensional time-space fractional Schr$ \bf{\ddot o}$dinger models, Optical and Quantum Electronics, 50 (2018), 32. Google Scholar |
[28] |
M. Ekici, A. Sonmezoglu, Q. Zhou, S. P. Moshokoa, M. Z. Ullah, A. H. Arnous, A. Biswas and M. Belic,
Analysis of optical solitons in nonlinear negative-indexed materials with anti-cubic nonlinearity, Opt. Quant. Electron., 50 (2018), 75.
doi: 10.1007/s11082-018-1341-3. |
[29] |
M. Ekici, M. Mirzazadeh, A. Sonmezoglu, Q. Zhou, S. P. Moshokoa, A. Biswas and M. Belic,
Dark and singular optical solitons with Kundu-Eckhaus equation by extended trial equation method and extended $G'/G$–expansion scheme, Optik, 127 (2016), 10490-10497.
doi: 10.1016/j.ijleo.2016.08.074. |
[30] |
M. Ekici, M. Mirzazadeh, M. Eslami, Q. Zhou, S. P. Moshokoa, A. Biswas and M. Belic,
Optical soliton perturbation with fractional-temporal evolution by first integral method with conformable fractional derivatives, Optik, 127 (2016), 10659-10669.
doi: 10.1016/j.ijleo.2016.08.076. |
[31] |
A. Esen, T. A. Sulaiman, H. Bulut and H. M. Baskonus, Optical solitons to the space-time fractional (1+1)-dimensional coupled nonlinear Schr$ \bf{\ddot o}$dinger equation, Optik, 167 (2018), 150-156. Google Scholar |
[32] |
M. Eslami, M. Mirzazadeh, B. F. Vajargah and A. Biswas, Optical solitons for the resonant nonlinear Schr$ \bf{\ddot o}$dinger's equation with time-dependent coefficients by the first integral method, Optik, 125 (2014), 3107-3116. Google Scholar |
[33] |
M. Eslami and M. Mirzazadeh,
Optical solitons with Biswas-Milovic equation for power law and dual-power law nonlinearities, Nonlinear Dyn., 83 (2016), 731-738.
doi: 10.1007/s11071-015-2361-1. |
[34] |
M. Eslami,
Soliton-like solutions for the coupled Schrodinger-Boussinesq equation, Optik, 126 (2016), 3987-3991.
doi: 10.1016/j.ijleo.2015.07.197. |
[35] |
M. Eslami,
Trial solution technique to chiral nonlinear Schr$ \bf{\ddot o}$dinger equation in (1+2)-dimensions, Nonlinear Dyn., 85 (2016), 813-816.
doi: 10.1007/s11071-016-2724-2. |
[36] |
M. Eslami, H. Rezazadeh, M. Rezazadeh and S. S. Mosavi, Exact solutions to the space-time fractional Schr$ \bf{\ddot o}$dinger-Hirota equation and the space-time modified KDV-Zakharov-Kuznetsov equation, Optical and Quantum Electronics, 49 (2017), 279. Google Scholar |
[37] |
M. Eslami and H. Rezazadeh,
The first integral method for Wu-Zhang system with conformable time-fractional derivative, Calcolo, 53 (2016), 475-485.
doi: 10.1007/s10092-015-0158-8. |
[38] |
O. A. Ilhan, H. Bulut, T. A. Sulaiman and H. M. Baskonus,
Dynamic of solitary wave solutions in some nonlinear pseudoparabolic models and Dodd-Bullough-Mikhailov equation, Indian Journal of Physics, 92 (2018), 999-1007.
doi: 10.1007/s12648-018-1187-3. |
[39] |
R. Khalil, M. Al Horani, A. Yousef and M. Sababheh,
A new definition of fractional derivative, Journal of Computational and Applied Mathematics, 264 (2014), 65-70.
doi: 10.1016/j.cam.2014.01.002. |
[40] |
J. Manafian, Optical soliton solutions for Schrdinger type nonlinear evolution equations by the $tan(\varphi/2)$-expansion method, Optik, 127 (2016), 4222-4245. Google Scholar |
[41] |
J. Manafian and M. F. Aghdaei, Abundant soliton solutions for the coupled Schr$ \bf{\ddot o}$dinger-Boussinesq system via an analytical method, The European Physical Journal Plus, 131 (2016), 97. Google Scholar |
[42] |
M. Mirzazadeh, M. Ekici, A. Sonmezoglu, M. Eslami, Q. Zhou, E. Zerrad, A. Biswas and M. Belic,
Optical Solitons in Nano-Fibers with Fractional Temporal Evolution, Journal of Computational and Theoretical Nanoscience, 13 (2016), 5361-5374.
doi: 10.1166/jctn.2016.5425. |
[43] |
K. M. Owolabi and A. Atangana, Numerical solution of fractional-in-space nonlinear Schr$ \bf{\ddot o}$dinger equation with the Riesz fractional derivative, The European Physical Journal Plus, 131 (2016), 335. Google Scholar |
[44] |
I. Podlubny, Fractional Differential Equations, 1$^{st}$ edition, Academic Press, an Diego, 1999.
doi: 10.1007/978-1-4612-0873-0.![]() ![]() |
[45] |
A. Sardar, K. Ali, S. T.R. Rizvi, M. Younis, Q. Zhou, E. Zerrad, A. Biswas and A. Bhrawy, Dispersive optical solitons in nanofibers with Schr$ \bf{\ddot o}$dinger-Hirota equation, Journal of Nanoelectronics and Optoelectronics, 11 (2016), 382-387. Google Scholar |
[46] |
M. Savescu, A. H. Bhrawy, E. M. Hilal, A. A. Alshaery and A. Biswas, Optical solitons in birefringent fibers with four-wave mixing for Kerr law nonlinearity, Rom. J. Phys., 59 (2014), 582-589. Google Scholar |
[47] |
A. R. Seadawy, Modulation instability analysis for the generalized derivative higher order nonlinear Shr$ \bf{\ddot o}$dinger equation and its the bright and dark soliton solutions, Journal of Electromagnetic Waves and Applications, 31 (2017), 1353-1362. Google Scholar |
[48] |
A. R. Seadawy and D. Lu, Bright and dark solitary wave soliton solutions for the generalized higher order nonlinear Shr$ \bf{\ddot o}$dinger equation and its stability, Results Phys., 7 (2017), 43-48. Google Scholar |
[49] |
T. A. Sulaiman, T. Akturk, H. Bulut and H. M. Baskonus,
Investigation of various soliton solutions to the Heisenberg ferromagnetic spin chain equation, Journal of Electromagnetic Waves and Applications, 32 (2018), 1093-1105.
doi: 10.1080/09205071.2017.1417919. |
[50] |
H. Triki and A. M. Wazwaz,
New solitons and periodic wave solutions for the (2+1)-dimensional Heisenberg ferromagnetic spin chain equation, Journal of Electromagnetic Waves and Applications, 30 (2016), 788-794.
doi: 10.1080/09205071.2016.1153986. |
[51] |
X. Xian-Lin and T. Jia-Shi,
Travelling wave solutions for Konopelchenko-Dubrovsky equation using an extended sinh-Gordon equation expansion method, Commun. Theor. Phys., 50 (2008), 1047-1051.
doi: 10.1088/0253-6102/50/5/06. |
[52] |
X. J. Yang, F. Gao and H. M. Srivastava,
Exact Travelling Wave solutions for the Local Fractional Two-Dimensional Burgers-Type Equations, Computers and Mathematics with Applications, 73 (2017), 203-210.
doi: 10.1016/j.camwa.2016.11.012. |
[53] |
H. C. Yaslan,
New analytic solutions of the conformable space-time fractional Kawahara equation, Optik, 140 (2017), 123-126.
doi: 10.1016/j.ijleo.2017.04.015. |
[54] |
R. Yilmaza and E. Bas, Explicit Solutions of Fractional Schr$ \bf{\ddot o}$dinger Equation via Fractional Calculus Operators, Int. J. Open Problems Compt. Math., 5 (2012), 133-141. Google Scholar |
[55] |
A. Yokus, H. M. Baskonus, T. A. Sulaiman and H. Bulut,
Numerical simulation and solutions of the two-component second order KdV evolutionary system, Numer Methods Partial Differential Eq., 34 (2018), 211-227.
doi: 10.1002/num.22192. |
[56] |
M. Younis, N. Cheemaa, S. A. Mahmood and S. T. R. Rizvi, On optical solitons: The chiral nonlinear Schr$ \bf{\ddot o}$dinger equation with perturbation and Bohm potential, Opt Quant Electron, 48 (2016), 542. Google Scholar |
[57] |
Q. Zhou,
Optical solitons for Biswas-Milovic model with Kerr law and parabolic law nonlinearities, Nonlinear Dynamics, 84 (2016), 677-681.
doi: 10.1007/s11071-015-2516-0. |
[58] |
Q. Zhou and A. Biswas,
Optical solitons in parity-time-symmetric mixed linear and nonlinear lattice with non-Kerr law nonlinearity, Superlattices Microstruct., 109 (2017), 588-598.
doi: 10.1016/j.spmi.2017.05.049. |
[59] |
Q. Zhou, A. Sonmezoglu, M. Ekici and M. Mirzazadeh,
Optical solitons of some fractional differential equations in nonlinear optics, J. Mod. Opt., 64 (2017), 2345-2349.
doi: 10.1080/09500340.2017.1357856. |
[60] |
Q. Zhou,
Analytical study on optical solitons in s kerr-law medium with an imprinted parity-time-symmetric mixed linear-nonliear lattice, Proc. Rom. Acad. Ser. A, 18 (2017), 223-230.
|
[61] |
Q. Zhou, C. Wei, H. Zhang, J. Lu, H. Yu, P. Yao and Q. Zhu,
Exact solutions to the resonant nonlinear schr$ \bf{\ddot o}$dinger equation with both spatio-temporal and inter-modal dispersions, Proc. Rom. Acad. Ser. A, 17 (2016), 307-313.
|
show all references
References:
[1] |
A. Abdon and B. Dumitru, New fractional derivatives with nonlocal and non-singular kernel: Theory and application to heat transfer model, Thermal Science, 20 (2016), 763-769. Google Scholar |
[2] |
M. A. Akinlar and M. Kurulay, A novel method for analytical solutions of fractional partial differential equations, Mathematical Problems in Engineering, 2013 (2013), Art. ID 195708, 4 pp.
doi: 10.1155/2013/195708. |
[3] |
K. K. Ali, R. I. Nuruddeen and K. R. Raslan,
New structures for the space-time fractional simplified MCH and SRLW equations, Chaos, Solitons and Fractals, 106 (2018), 304-309.
doi: 10.1016/j.chaos.2017.11.038. |
[4] |
S. Arbabi and M. Najafi, Exact solitary wave solutions of the complex nonlinear Schr$ \bf{\ddot o}$dinger equations, Optik, 127 (2016), 4682-4688. Google Scholar |
[5] |
A. H. Arnous, M. Z. Ullah, M. Asma, S. P. Moshokoa, Q. Zhou, M. Mirzazadeh, A. Biswas and M. Belic, Dark and singular dispersive optical solitons of Schr$ \bf{\ddot o}$dinger-Hirota equation by modified simple equation method, Optik, 136 (2017), 445-450. Google Scholar |
[6] |
M. Arshad, A. R. Seadawy and D. Lu, Elliptic function and solitary wave solutions of the higher-order nonlinear Schr$ \bf{\ddot o}$dinger dynamical equation with fourth-order dispersion and cubic-quintic nonlinearity and its stability, The European Physical Journal Plus, 132 (2017), 371. Google Scholar |
[7] |
A. Atangana and D. Baleanu,
Application of Fixed Point Theorem for Stability Analysis of a Nonlinear Schrodinger with Caputo-Liouville Derivatives, Filomat, 31 (2017), 2243-2248.
doi: 10.2298/FIL1708243A. |
[8] |
E. Bas, R. Yilmaza and E. Panakhov, Fractional solutions of bessel equation with $N$-method, The Scientific World Journal, 2013 (2013), Article ID 685695, 8 pages.
doi: 10.1155/2013/685695. |
[9] |
H. M. Baskonus, T. A. Sulaiman, H. Bulut and T. Akturk, Investigations of dark, bright, combined dark-bright optical and other soliton solutions in the complex cubic nonlinear Schr$ \bf{\ddot o}$dinger equation with $\delta$-potential, Superlattices and Microstructures, 115 (2016), 19-29. Google Scholar |
[10] |
H. M. Baskonus, H. Bulut and T. A. Sulaiman,
Investigation of various travelling wave solutions to the extended (2+1)-dimensional quantum ZK equation, The European Physical Journal Plus, 132 (2017), 482.
doi: 10.1140/epjp/i2017-11778-y. |
[11] |
H. M. Baskonus, T. A. Sulaiman and H. Bulut, Dark, bright and other optical solitons to the decoupled nonlinear Schr$ \bf{\ddot o}$dinger equation arising in dual-core optical fibers, Opt Quant Electron, 50 (2018), 165. Google Scholar |
[12] |
H. M. Baskonus, T. A. Sulaiman and H. Bulut,
Bright, dark optical and other solitons to the generalized higher-order NLSE in optical fibers, Opt Quant Electron, 50 (2018), 253.
doi: 10.1007/s11082-018-1522-0. |
[13] |
I. Bendahmane, H. Triki, A. Biswas, A. S. Alshomrani, Q. Zhou, S. P. Moshokoa and M. Belic, Bright, dark and W-shaped solitons with extended nonlinear Schr$ \bf{\ddot o}$dinger's equation for odd and even higher-order terms, Superlattices Microstruct., 114 (2018), 53-61. Google Scholar |
[14] |
A. H. Bhrawy, A. A. Alshaery, E. M. Hilal, Z. Jovanoski and A. Biswas,
Bright and dark solitons in a cascaded system, Optik, 125 (2014), 6162-6165.
doi: 10.1016/j.ijleo.2014.06.118. |
[15] |
A. Biswas, M. Ekici, A. Sonmezoglu, Q. Zhou, S. P. Moshokoa and M. Belic,
Optical soliton perturbation with full nonlinearity for Kundu-Eckhaus equation by extended trial function scheme, Optik, 160 (2018), 17-23.
doi: 10.1016/j.ijleo.2018.01.111. |
[16] |
A. Biswas, Q. Zhou, S. P. Moshokoa, H. Triki, M. Belic and R. T. Alqahtani,
Resonant 1-soliton solution in anti-cubic nonlinear medium with perturbations, Optik, 145 (2017), 14-17.
doi: 10.1016/j.ijleo.2017.07.036. |
[17] |
A. Biswas, Q. Zhou, M. Z. Ullah, H. Triki, S. P. Moshokoa and M. Belic,
Optical soliton perturbation with anti-cubic nonlinearity by semi-inverse variational principle, Optik, 143 (2017), 131-134.
doi: 10.1016/j.ijleo.2017.06.087. |
[18] |
A. Biswas, A. H. Kara, M. Z. Ullah, Q. Zhou, H. Triki and M. Belic,
Conservation laws for cubic-quartic optical solitons in Kerr and power law media, Optik, 145 (2017), 650-654.
doi: 10.1016/j.ijleo.2017.08.047. |
[19] |
A. Biswas, H. Triki, Q. Zhou, S. P. Moshokoa, M. Z. Ullah and M. Belic,
Cubic-quartic optical solitons in Kerr and power law media, Commun. Theor. Phys., 144 (2017), 357-362.
doi: 10.1016/j.ijleo.2017.07.008. |
[20] |
H. Bulut, T. A. Sulaiman and B. Demirdag, Dynamics of soliton solutions in the chiral nonlinear Schr$ \bf{\ddot o}$dinger equations, Nonlinear Dynamics, 91 (2018), 1985-1991. Google Scholar |
[21] |
H. Bulut, T. A. Sulaiman, H. M. Baskonus and T. Akturk,
Complex acoustic gravity wave behaviors to some mathematical models arising in fluid dynamics and nonlinear dispersive media, Opt Quant Electron, 50 (2018), 19.
doi: 10.1007/s11082-017-1286-y. |
[22] |
H. Bulut, T. A. Sulaiman, H. M. Baskonus, H. Rezazadeh, M. Eslami and M. Mirzazadeh,
Optical solitons and other solutions to the conformable space-time fractional Fokas-Lenells equation, Optik, 127 (2018), 20-27.
doi: 10.1016/j.ijleo.2018.06.108. |
[23] |
H. Bulut, T. A. Sulaiman and H. M. Baskonus,
On the new soliton and optical wave structures to some nonlinear evolution equation, The European Physical Journal Plus, 132 (2017), 459.
doi: 10.1140/epjp/i2017-11738-7. |
[24] |
C. Cattani,
Harmonic wavelet solutions of the Schrodinger equation, International Journal of Fluid Mechanics Research, 30 (2003), 463-472.
doi: 10.1615/InterJFluidMechRes.v30.i5.10. |
[25] |
C. Cattani, T. A. Sulaiman, H. M. Baskonus and H. Bulut,
Solitons in an inhomogeneous Murnaghan's rod, Eur. Phys. J. Plus, 133 (2018), 228.
doi: 10.1140/epjp/i2018-12085-y. |
[26] |
C. Cattani, T. A. Sulaiman, H. M. Baskonus and H. Bulut,
On the soliton solutions to the Nizhnik-Novikov-Veselov and the Drinfel'd-Sokolov systems, Opt Quant Electron, 50 (2018), 138.
doi: 10.1007/s11082-018-1406-3. |
[27] |
M. T. Darvishi, S. Ahmadian, S. B. Arbabi and M. Najafi, Optical solitons for a family of nonlinear (1+1)-dimensional time-space fractional Schr$ \bf{\ddot o}$dinger models, Optical and Quantum Electronics, 50 (2018), 32. Google Scholar |
[28] |
M. Ekici, A. Sonmezoglu, Q. Zhou, S. P. Moshokoa, M. Z. Ullah, A. H. Arnous, A. Biswas and M. Belic,
Analysis of optical solitons in nonlinear negative-indexed materials with anti-cubic nonlinearity, Opt. Quant. Electron., 50 (2018), 75.
doi: 10.1007/s11082-018-1341-3. |
[29] |
M. Ekici, M. Mirzazadeh, A. Sonmezoglu, Q. Zhou, S. P. Moshokoa, A. Biswas and M. Belic,
Dark and singular optical solitons with Kundu-Eckhaus equation by extended trial equation method and extended $G'/G$–expansion scheme, Optik, 127 (2016), 10490-10497.
doi: 10.1016/j.ijleo.2016.08.074. |
[30] |
M. Ekici, M. Mirzazadeh, M. Eslami, Q. Zhou, S. P. Moshokoa, A. Biswas and M. Belic,
Optical soliton perturbation with fractional-temporal evolution by first integral method with conformable fractional derivatives, Optik, 127 (2016), 10659-10669.
doi: 10.1016/j.ijleo.2016.08.076. |
[31] |
A. Esen, T. A. Sulaiman, H. Bulut and H. M. Baskonus, Optical solitons to the space-time fractional (1+1)-dimensional coupled nonlinear Schr$ \bf{\ddot o}$dinger equation, Optik, 167 (2018), 150-156. Google Scholar |
[32] |
M. Eslami, M. Mirzazadeh, B. F. Vajargah and A. Biswas, Optical solitons for the resonant nonlinear Schr$ \bf{\ddot o}$dinger's equation with time-dependent coefficients by the first integral method, Optik, 125 (2014), 3107-3116. Google Scholar |
[33] |
M. Eslami and M. Mirzazadeh,
Optical solitons with Biswas-Milovic equation for power law and dual-power law nonlinearities, Nonlinear Dyn., 83 (2016), 731-738.
doi: 10.1007/s11071-015-2361-1. |
[34] |
M. Eslami,
Soliton-like solutions for the coupled Schrodinger-Boussinesq equation, Optik, 126 (2016), 3987-3991.
doi: 10.1016/j.ijleo.2015.07.197. |
[35] |
M. Eslami,
Trial solution technique to chiral nonlinear Schr$ \bf{\ddot o}$dinger equation in (1+2)-dimensions, Nonlinear Dyn., 85 (2016), 813-816.
doi: 10.1007/s11071-016-2724-2. |
[36] |
M. Eslami, H. Rezazadeh, M. Rezazadeh and S. S. Mosavi, Exact solutions to the space-time fractional Schr$ \bf{\ddot o}$dinger-Hirota equation and the space-time modified KDV-Zakharov-Kuznetsov equation, Optical and Quantum Electronics, 49 (2017), 279. Google Scholar |
[37] |
M. Eslami and H. Rezazadeh,
The first integral method for Wu-Zhang system with conformable time-fractional derivative, Calcolo, 53 (2016), 475-485.
doi: 10.1007/s10092-015-0158-8. |
[38] |
O. A. Ilhan, H. Bulut, T. A. Sulaiman and H. M. Baskonus,
Dynamic of solitary wave solutions in some nonlinear pseudoparabolic models and Dodd-Bullough-Mikhailov equation, Indian Journal of Physics, 92 (2018), 999-1007.
doi: 10.1007/s12648-018-1187-3. |
[39] |
R. Khalil, M. Al Horani, A. Yousef and M. Sababheh,
A new definition of fractional derivative, Journal of Computational and Applied Mathematics, 264 (2014), 65-70.
doi: 10.1016/j.cam.2014.01.002. |
[40] |
J. Manafian, Optical soliton solutions for Schrdinger type nonlinear evolution equations by the $tan(\varphi/2)$-expansion method, Optik, 127 (2016), 4222-4245. Google Scholar |
[41] |
J. Manafian and M. F. Aghdaei, Abundant soliton solutions for the coupled Schr$ \bf{\ddot o}$dinger-Boussinesq system via an analytical method, The European Physical Journal Plus, 131 (2016), 97. Google Scholar |
[42] |
M. Mirzazadeh, M. Ekici, A. Sonmezoglu, M. Eslami, Q. Zhou, E. Zerrad, A. Biswas and M. Belic,
Optical Solitons in Nano-Fibers with Fractional Temporal Evolution, Journal of Computational and Theoretical Nanoscience, 13 (2016), 5361-5374.
doi: 10.1166/jctn.2016.5425. |
[43] |
K. M. Owolabi and A. Atangana, Numerical solution of fractional-in-space nonlinear Schr$ \bf{\ddot o}$dinger equation with the Riesz fractional derivative, The European Physical Journal Plus, 131 (2016), 335. Google Scholar |
[44] |
I. Podlubny, Fractional Differential Equations, 1$^{st}$ edition, Academic Press, an Diego, 1999.
doi: 10.1007/978-1-4612-0873-0.![]() ![]() |
[45] |
A. Sardar, K. Ali, S. T.R. Rizvi, M. Younis, Q. Zhou, E. Zerrad, A. Biswas and A. Bhrawy, Dispersive optical solitons in nanofibers with Schr$ \bf{\ddot o}$dinger-Hirota equation, Journal of Nanoelectronics and Optoelectronics, 11 (2016), 382-387. Google Scholar |
[46] |
M. Savescu, A. H. Bhrawy, E. M. Hilal, A. A. Alshaery and A. Biswas, Optical solitons in birefringent fibers with four-wave mixing for Kerr law nonlinearity, Rom. J. Phys., 59 (2014), 582-589. Google Scholar |
[47] |
A. R. Seadawy, Modulation instability analysis for the generalized derivative higher order nonlinear Shr$ \bf{\ddot o}$dinger equation and its the bright and dark soliton solutions, Journal of Electromagnetic Waves and Applications, 31 (2017), 1353-1362. Google Scholar |
[48] |
A. R. Seadawy and D. Lu, Bright and dark solitary wave soliton solutions for the generalized higher order nonlinear Shr$ \bf{\ddot o}$dinger equation and its stability, Results Phys., 7 (2017), 43-48. Google Scholar |
[49] |
T. A. Sulaiman, T. Akturk, H. Bulut and H. M. Baskonus,
Investigation of various soliton solutions to the Heisenberg ferromagnetic spin chain equation, Journal of Electromagnetic Waves and Applications, 32 (2018), 1093-1105.
doi: 10.1080/09205071.2017.1417919. |
[50] |
H. Triki and A. M. Wazwaz,
New solitons and periodic wave solutions for the (2+1)-dimensional Heisenberg ferromagnetic spin chain equation, Journal of Electromagnetic Waves and Applications, 30 (2016), 788-794.
doi: 10.1080/09205071.2016.1153986. |
[51] |
X. Xian-Lin and T. Jia-Shi,
Travelling wave solutions for Konopelchenko-Dubrovsky equation using an extended sinh-Gordon equation expansion method, Commun. Theor. Phys., 50 (2008), 1047-1051.
doi: 10.1088/0253-6102/50/5/06. |
[52] |
X. J. Yang, F. Gao and H. M. Srivastava,
Exact Travelling Wave solutions for the Local Fractional Two-Dimensional Burgers-Type Equations, Computers and Mathematics with Applications, 73 (2017), 203-210.
doi: 10.1016/j.camwa.2016.11.012. |
[53] |
H. C. Yaslan,
New analytic solutions of the conformable space-time fractional Kawahara equation, Optik, 140 (2017), 123-126.
doi: 10.1016/j.ijleo.2017.04.015. |
[54] |
R. Yilmaza and E. Bas, Explicit Solutions of Fractional Schr$ \bf{\ddot o}$dinger Equation via Fractional Calculus Operators, Int. J. Open Problems Compt. Math., 5 (2012), 133-141. Google Scholar |
[55] |
A. Yokus, H. M. Baskonus, T. A. Sulaiman and H. Bulut,
Numerical simulation and solutions of the two-component second order KdV evolutionary system, Numer Methods Partial Differential Eq., 34 (2018), 211-227.
doi: 10.1002/num.22192. |
[56] |
M. Younis, N. Cheemaa, S. A. Mahmood and S. T. R. Rizvi, On optical solitons: The chiral nonlinear Schr$ \bf{\ddot o}$dinger equation with perturbation and Bohm potential, Opt Quant Electron, 48 (2016), 542. Google Scholar |
[57] |
Q. Zhou,
Optical solitons for Biswas-Milovic model with Kerr law and parabolic law nonlinearities, Nonlinear Dynamics, 84 (2016), 677-681.
doi: 10.1007/s11071-015-2516-0. |
[58] |
Q. Zhou and A. Biswas,
Optical solitons in parity-time-symmetric mixed linear and nonlinear lattice with non-Kerr law nonlinearity, Superlattices Microstruct., 109 (2017), 588-598.
doi: 10.1016/j.spmi.2017.05.049. |
[59] |
Q. Zhou, A. Sonmezoglu, M. Ekici and M. Mirzazadeh,
Optical solitons of some fractional differential equations in nonlinear optics, J. Mod. Opt., 64 (2017), 2345-2349.
doi: 10.1080/09500340.2017.1357856. |
[60] |
Q. Zhou,
Analytical study on optical solitons in s kerr-law medium with an imprinted parity-time-symmetric mixed linear-nonliear lattice, Proc. Rom. Acad. Ser. A, 18 (2017), 223-230.
|
[61] |
Q. Zhou, C. Wei, H. Zhang, J. Lu, H. Yu, P. Yao and Q. Zhu,
Exact solutions to the resonant nonlinear schr$ \bf{\ddot o}$dinger equation with both spatio-temporal and inter-modal dispersions, Proc. Rom. Acad. Ser. A, 17 (2016), 307-313.
|








[1] |
Abdollah Borhanifar, Maria Alessandra Ragusa, Sohrab Valizadeh. High-order numerical method for two-dimensional Riesz space fractional advection-dispersion equation. Discrete & Continuous Dynamical Systems - B, 2020 doi: 10.3934/dcdsb.2020355 |
[2] |
Thierry Cazenave, Ivan Naumkin. Local smooth solutions of the nonlinear Klein-gordon equation. Discrete & Continuous Dynamical Systems - S, 2020 doi: 10.3934/dcdss.2020448 |
[3] |
Zheng Han, Daoyuan Fang. Almost global existence for the Klein-Gordon equation with the Kirchhoff-type nonlinearity. Communications on Pure & Applied Analysis, 2021, 20 (2) : 737-754. doi: 10.3934/cpaa.2020287 |
[4] |
François Dubois. Third order equivalent equation of lattice Boltzmann scheme. Discrete & Continuous Dynamical Systems - A, 2009, 23 (1&2) : 221-248. doi: 10.3934/dcds.2009.23.221 |
[5] |
Anh Tuan Duong, Phuong Le, Nhu Thang Nguyen. Symmetry and nonexistence results for a fractional Choquard equation with weights. Discrete & Continuous Dynamical Systems - A, 2021, 41 (2) : 489-505. doi: 10.3934/dcds.2020265 |
[6] |
Kevin Li. Dynamic transitions of the Swift-Hohenberg equation with third-order dispersion. Discrete & Continuous Dynamical Systems - B, 2020 doi: 10.3934/dcdsb.2021003 |
[7] |
Xuefeng Zhang, Yingbo Zhang. Fault-tolerant control against actuator failures for uncertain singular fractional order systems. Numerical Algebra, Control & Optimization, 2021, 11 (1) : 1-12. doi: 10.3934/naco.2020011 |
[8] |
Reza Chaharpashlou, Abdon Atangana, Reza Saadati. On the fuzzy stability results for fractional stochastic Volterra integral equation. Discrete & Continuous Dynamical Systems - S, 2020 doi: 10.3934/dcdss.2020432 |
[9] |
Vo Van Au, Hossein Jafari, Zakia Hammouch, Nguyen Huy Tuan. On a final value problem for a nonlinear fractional pseudo-parabolic equation. Electronic Research Archive, 2021, 29 (1) : 1709-1734. doi: 10.3934/era.2020088 |
[10] |
Kihoon Seong. Low regularity a priori estimates for the fourth order cubic nonlinear Schrödinger equation. Communications on Pure & Applied Analysis, 2020, 19 (12) : 5437-5473. doi: 10.3934/cpaa.2020247 |
[11] |
Van Duong Dinh. Random data theory for the cubic fourth-order nonlinear Schrödinger equation. Communications on Pure & Applied Analysis, 2021, 20 (2) : 651-680. doi: 10.3934/cpaa.2020284 |
[12] |
Andrea Braides, Antonio Tribuzio. Perturbed minimizing movements of families of functionals. Discrete & Continuous Dynamical Systems - S, 2021, 14 (1) : 373-393. doi: 10.3934/dcdss.2020324 |
[13] |
Leilei Wei, Yinnian He. A fully discrete local discontinuous Galerkin method with the generalized numerical flux to solve the tempered fractional reaction-diffusion equation. Discrete & Continuous Dynamical Systems - B, 2020 doi: 10.3934/dcdsb.2020319 |
[14] |
S. Sadeghi, H. Jafari, S. Nemati. Solving fractional Advection-diffusion equation using Genocchi operational matrix based on Atangana-Baleanu derivative. Discrete & Continuous Dynamical Systems - S, 2020 doi: 10.3934/dcdss.2020435 |
[15] |
Lihong Zhang, Wenwen Hou, Bashir Ahmad, Guotao Wang. Radial symmetry for logarithmic Choquard equation involving a generalized tempered fractional $ p $-Laplacian. Discrete & Continuous Dynamical Systems - S, 2020 doi: 10.3934/dcdss.2020445 |
[16] |
Jean-Claude Saut, Yuexun Wang. Long time behavior of the fractional Korteweg-de Vries equation with cubic nonlinearity. Discrete & Continuous Dynamical Systems - A, 2021, 41 (3) : 1133-1155. doi: 10.3934/dcds.2020312 |
[17] |
Peter Frolkovič, Viera Kleinová. A new numerical method for level set motion in normal direction used in optical flow estimation. Discrete & Continuous Dynamical Systems - S, 2021, 14 (3) : 851-863. doi: 10.3934/dcdss.2020347 |
[18] |
Karol Mikula, Jozef Urbán, Michal Kollár, Martin Ambroz, Ivan Jarolímek, Jozef Šibík, Mária Šibíková. An automated segmentation of NATURA 2000 habitats from Sentinel-2 optical data. Discrete & Continuous Dynamical Systems - S, 2021, 14 (3) : 1017-1032. doi: 10.3934/dcdss.2020348 |
[19] |
Li-Bin Liu, Ying Liang, Jian Zhang, Xiaobing Bao. A robust adaptive grid method for singularly perturbed Burger-Huxley equations. Electronic Research Archive, 2020, 28 (4) : 1439-1457. doi: 10.3934/era.2020076 |
[20] |
Marco Ghimenti, Anna Maria Micheletti. Compactness results for linearly perturbed Yamabe problem on manifolds with boundary. Discrete & Continuous Dynamical Systems - S, 2020 doi: 10.3934/dcdss.2020453 |
2019 Impact Factor: 1.233
Tools
Metrics
Other articles
by authors
[Back to Top]