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Dynamics of shallow water waves with Gardner-Kadomtsev-Petviashvili equation
1. | Computer Engineering Technique Department Al-Rafidain, University College, Baghdad, Iraq |
2. | Department of Engineering Sciences, Faculty of Technology and Engineering East of Guilan, University of Guilan, P.C. 44891-63157, Rudsar-Vajargah, Iran |
3. | Department of Mathematical Sciences, Delaware State University, Dover, DE 19901-2277, United States |
References:
[1] |
M. Antonova and A. Biswas, Adiabatic parameter dynamics of perturbed solitons,, Communications in Nonlinear Science and Numerical Simulation, 14 (2009), 734.
doi: 10.1016/j.cnsns.2007.12.004. |
[2] |
A. H. Bhrawy, M. A. Abdelkawy, S. Kumar and A. Biswas, Solitons and other solutions to Kadomtsev-Petviashvili equation of B-type,, Romanian Journal of Physics, 58 (2013), 729.
|
[3] |
A. Biswas and E. Zerrad, Soliton perturbation theory for the Gardner equation,, Advanced Studies in Theoretical Physics, 2 (2008), 787.
|
[4] |
A. Biswas and A. Ranasinghe, 1-soliton solution of Kadomtsev-Petviashvili equation with power law nonlinearity,, Applied Mathematics and Computation, 214 (2009), 645.
doi: 10.1016/j.amc.2009.04.001. |
[5] |
A. Biswas and A. Ranasinghe, Topological 1-soliton solution of Kadomtsev-Petviashvili equation with power law nonlinearity,, Applied Mathematics and Computation, 217 (2010), 1771.
doi: 10.1016/j.amc.2009.09.042. |
[6] |
R. Choudhury and S. K. Das, Viscelastic MHD free convective flow through porous media in presence of radiation and chemical reaction with heat and mass transfer,, Journal of Applied Fluid Mechanics, 7 (2014), 603. Google Scholar |
[7] |
G. Ebadi, N. Y. Fard, A. H. Bhrawy, S. Kumar, H. Triki, A. Yildirim and A. Biswas, Solitons and other solutions to (3+1)-dimensional extended Kadomtsev-Petviashvili equation with power law nonlinearity,, Romaninan Reports in Physics, 65 (2013), 27. Google Scholar |
[8] |
M. Eslami, M. Mirzazadeh and A. Biswas, Soliton solutions of the resonant nonlinear Schrodinger's equation in optical fibers with time-dependent coefficients by simplest equation approach,, Journal of Modern Optics, 60 (2013), 1627.
doi: 10.1080/09500340.2013.850777. |
[9] |
M. Eslami and M. Mirzazadeh, Topological 1-soliton solution of nonlinear Schrodinger equation with dual-power law nonlinearity in nonlinear optical fibers,, European Physical Journal, 128 (2013). Google Scholar |
[10] |
E. V. Krishnan, H. Triki, M. Labidi and A. Biswas, A study of shallow water waves with Gardner's equation,, Nonlinear Dynamics, 66 (2011), 497.
doi: 10.1007/s11071-010-9928-7. |
[11] |
S. Kundu and K. Ghoshal, An explicit model for concentration distribution using biquadratic log-wake law in an open channel flow,, Journal of Applied Fluid Mechanics, 6 (2013), 339. Google Scholar |
[12] |
Z. G. Makukula and S. S. Motsa, Spectral homotopy analysis method for PDEs that model the unsteady Von Karma swirling flow,, Journal of Applied Fluid Mechanics, 7 (2014), 711. Google Scholar |
[13] |
M. Mirzazadeh, M. Eslami and A. Biswas, Soliton solutions of the generalized Klein-Gordon equation by using ${G'}/G$-expansion method,, Computational and Applied Mathematics, 33 (2014), 831.
doi: 10.1007/s40314-013-0098-3. |
[14] |
M. Mirzazadeh and M. Eslami, Exact solutions for nonlinear variants of Kadomtsev-Petviashvili (n, n) equation using functional variable method,, Pramana, 81 (2013), 225. Google Scholar |
[15] |
A. Nazarzadeh, M. Eslami and M. Mirzazadeh, Exact solutions of some nonlinear partial differential equations using functional variable method,, Pramana, 81 (2013), 225.
doi: 10.1007/s12043-013-0565-9. |
[16] |
D. Pal and S. Chatterjee, Effects of radiation on Darcey-Forchheimer convective flow over a stretching sheet in a micropolar fluid with a non-uniform heat source/sink,, Journal of Applied Fluid Mechanics, 8 (2015), 207. Google Scholar |
[17] |
P. Ram and V. Kumar, Rotationally symmetric ferrofluid flow and heat transfer in porous medium with variable viscosity and viscous dissipation,, Journal of Applied Fluid Mechanics, 7 (2014), 357. Google Scholar |
[18] |
S. M. Shafiof, Z. Bagheri and Sousaraei, New solutions for positive and negative Gardner-KP equations,, World Applied Science Journal, 13 (2011), 662. Google Scholar |
[19] |
N. Taghizadeh and M. Mirzazadeh, The simplest equation method to study perturbed nonlinear Schrodinger's equation with Kerr law nonlinearity,, Communications in Nonlinear Science and Numerical Simulations, 17 (2012), 1493.
doi: 10.1016/j.cnsns.2011.09.023. |
[20] |
N. Taghizadeh, M. Mirzazadeh and F. Farahrooz, Exact soliton solutions of the modified KdV-KP equation and the Burgers-KP equation by using the first integral method,, Applied Mathematical Modelling, 35 (2011), 3991.
doi: 10.1016/j.apm.2011.02.001. |
[21] |
N. Taghizadeh, M. Mirzazadeh and A. Samiei Paghaleh, Exact solutions of some nonlinear evolution equations via the first integral method,, Ain Shams Engineering Journal, 4 (2013), 493.
doi: 10.1016/j.asej.2012.10.002. |
[22] |
W. M. Taha, M. S. M. Noorani and I. Hashim, New exact solutions of sixth-order thin-film equation,, Journal of King Saud University- Science, 26 (2014), 75.
doi: 10.1016/j.jksus.2013.07.001. |
[23] |
F. Tascan, A. Bekir and M. Koparan, Travelling wave solutions of nonlinear evolutions by using the first integral method,, Communications in Nonlinear Science and Numerical Simulations, 14 (2009), 1810.
doi: 10.1016/j.cnsns.2008.07.009. |
[24] |
F. Tascan and A. Bekir, Travelling wave solutions of the Cahn-Allen equation by using first integral method,, Applied Mathematics and Computation, 207 (2009), 279.
doi: 10.1016/j.amc.2008.10.031. |
[25] |
H. Triki, B. J. M. Sturdevant, T. Hayat, O. M. Aldossary and A. Biswas, Shock wave solutions of the variants of Kadomtsev-Petviashvili equation,, Canadian Journal of Physics, 89 (2011), 979.
doi: 10.1139/p11-083. |
[26] |
M. L. Wang, X. Z. Li and J. L. Zhang, The ${G'}/G$-expansion method and travelling wave solutions of nonlinear evolution equations in mathematical physics,, Physics Letters A, 372 (2008), 417.
doi: 10.1016/j.physleta.2007.07.051. |
[27] |
A. M. Wazwaz, Solitons and singular solutions for the Gardner-KP equation,, Applied Mathematics and Computation, 204 (2008), 162.
doi: 10.1016/j.amc.2008.06.011. |
[28] |
A. Yildirim, A. Samiei Paghaleh, M. Mirzazadeh, H. Moosaei and A. Biswas, New exact travelling wave solutions for DS-I and DS-II equations,, Nonlinear Analysis: Modelling and Control, 17 (2012), 369.
|
[29] |
E. Zayed and K. A. Gepreel, Some applications of the ${G'}/G$-expansion method to non-linear partial differential equations,, Applied Mathematics and Computation, 212 (2009), 1.
doi: 10.1016/j.amc.2009.02.009. |
[30] |
J. Zhang, F. Jiang and X. Zhao, An improved ${G'}/G$-expansion method for solving nonlinear evolution equations,, International Journal of Computer Mathematics, 87 (2010), 1716.
doi: 10.1080/00207160802450166. |
show all references
References:
[1] |
M. Antonova and A. Biswas, Adiabatic parameter dynamics of perturbed solitons,, Communications in Nonlinear Science and Numerical Simulation, 14 (2009), 734.
doi: 10.1016/j.cnsns.2007.12.004. |
[2] |
A. H. Bhrawy, M. A. Abdelkawy, S. Kumar and A. Biswas, Solitons and other solutions to Kadomtsev-Petviashvili equation of B-type,, Romanian Journal of Physics, 58 (2013), 729.
|
[3] |
A. Biswas and E. Zerrad, Soliton perturbation theory for the Gardner equation,, Advanced Studies in Theoretical Physics, 2 (2008), 787.
|
[4] |
A. Biswas and A. Ranasinghe, 1-soliton solution of Kadomtsev-Petviashvili equation with power law nonlinearity,, Applied Mathematics and Computation, 214 (2009), 645.
doi: 10.1016/j.amc.2009.04.001. |
[5] |
A. Biswas and A. Ranasinghe, Topological 1-soliton solution of Kadomtsev-Petviashvili equation with power law nonlinearity,, Applied Mathematics and Computation, 217 (2010), 1771.
doi: 10.1016/j.amc.2009.09.042. |
[6] |
R. Choudhury and S. K. Das, Viscelastic MHD free convective flow through porous media in presence of radiation and chemical reaction with heat and mass transfer,, Journal of Applied Fluid Mechanics, 7 (2014), 603. Google Scholar |
[7] |
G. Ebadi, N. Y. Fard, A. H. Bhrawy, S. Kumar, H. Triki, A. Yildirim and A. Biswas, Solitons and other solutions to (3+1)-dimensional extended Kadomtsev-Petviashvili equation with power law nonlinearity,, Romaninan Reports in Physics, 65 (2013), 27. Google Scholar |
[8] |
M. Eslami, M. Mirzazadeh and A. Biswas, Soliton solutions of the resonant nonlinear Schrodinger's equation in optical fibers with time-dependent coefficients by simplest equation approach,, Journal of Modern Optics, 60 (2013), 1627.
doi: 10.1080/09500340.2013.850777. |
[9] |
M. Eslami and M. Mirzazadeh, Topological 1-soliton solution of nonlinear Schrodinger equation with dual-power law nonlinearity in nonlinear optical fibers,, European Physical Journal, 128 (2013). Google Scholar |
[10] |
E. V. Krishnan, H. Triki, M. Labidi and A. Biswas, A study of shallow water waves with Gardner's equation,, Nonlinear Dynamics, 66 (2011), 497.
doi: 10.1007/s11071-010-9928-7. |
[11] |
S. Kundu and K. Ghoshal, An explicit model for concentration distribution using biquadratic log-wake law in an open channel flow,, Journal of Applied Fluid Mechanics, 6 (2013), 339. Google Scholar |
[12] |
Z. G. Makukula and S. S. Motsa, Spectral homotopy analysis method for PDEs that model the unsteady Von Karma swirling flow,, Journal of Applied Fluid Mechanics, 7 (2014), 711. Google Scholar |
[13] |
M. Mirzazadeh, M. Eslami and A. Biswas, Soliton solutions of the generalized Klein-Gordon equation by using ${G'}/G$-expansion method,, Computational and Applied Mathematics, 33 (2014), 831.
doi: 10.1007/s40314-013-0098-3. |
[14] |
M. Mirzazadeh and M. Eslami, Exact solutions for nonlinear variants of Kadomtsev-Petviashvili (n, n) equation using functional variable method,, Pramana, 81 (2013), 225. Google Scholar |
[15] |
A. Nazarzadeh, M. Eslami and M. Mirzazadeh, Exact solutions of some nonlinear partial differential equations using functional variable method,, Pramana, 81 (2013), 225.
doi: 10.1007/s12043-013-0565-9. |
[16] |
D. Pal and S. Chatterjee, Effects of radiation on Darcey-Forchheimer convective flow over a stretching sheet in a micropolar fluid with a non-uniform heat source/sink,, Journal of Applied Fluid Mechanics, 8 (2015), 207. Google Scholar |
[17] |
P. Ram and V. Kumar, Rotationally symmetric ferrofluid flow and heat transfer in porous medium with variable viscosity and viscous dissipation,, Journal of Applied Fluid Mechanics, 7 (2014), 357. Google Scholar |
[18] |
S. M. Shafiof, Z. Bagheri and Sousaraei, New solutions for positive and negative Gardner-KP equations,, World Applied Science Journal, 13 (2011), 662. Google Scholar |
[19] |
N. Taghizadeh and M. Mirzazadeh, The simplest equation method to study perturbed nonlinear Schrodinger's equation with Kerr law nonlinearity,, Communications in Nonlinear Science and Numerical Simulations, 17 (2012), 1493.
doi: 10.1016/j.cnsns.2011.09.023. |
[20] |
N. Taghizadeh, M. Mirzazadeh and F. Farahrooz, Exact soliton solutions of the modified KdV-KP equation and the Burgers-KP equation by using the first integral method,, Applied Mathematical Modelling, 35 (2011), 3991.
doi: 10.1016/j.apm.2011.02.001. |
[21] |
N. Taghizadeh, M. Mirzazadeh and A. Samiei Paghaleh, Exact solutions of some nonlinear evolution equations via the first integral method,, Ain Shams Engineering Journal, 4 (2013), 493.
doi: 10.1016/j.asej.2012.10.002. |
[22] |
W. M. Taha, M. S. M. Noorani and I. Hashim, New exact solutions of sixth-order thin-film equation,, Journal of King Saud University- Science, 26 (2014), 75.
doi: 10.1016/j.jksus.2013.07.001. |
[23] |
F. Tascan, A. Bekir and M. Koparan, Travelling wave solutions of nonlinear evolutions by using the first integral method,, Communications in Nonlinear Science and Numerical Simulations, 14 (2009), 1810.
doi: 10.1016/j.cnsns.2008.07.009. |
[24] |
F. Tascan and A. Bekir, Travelling wave solutions of the Cahn-Allen equation by using first integral method,, Applied Mathematics and Computation, 207 (2009), 279.
doi: 10.1016/j.amc.2008.10.031. |
[25] |
H. Triki, B. J. M. Sturdevant, T. Hayat, O. M. Aldossary and A. Biswas, Shock wave solutions of the variants of Kadomtsev-Petviashvili equation,, Canadian Journal of Physics, 89 (2011), 979.
doi: 10.1139/p11-083. |
[26] |
M. L. Wang, X. Z. Li and J. L. Zhang, The ${G'}/G$-expansion method and travelling wave solutions of nonlinear evolution equations in mathematical physics,, Physics Letters A, 372 (2008), 417.
doi: 10.1016/j.physleta.2007.07.051. |
[27] |
A. M. Wazwaz, Solitons and singular solutions for the Gardner-KP equation,, Applied Mathematics and Computation, 204 (2008), 162.
doi: 10.1016/j.amc.2008.06.011. |
[28] |
A. Yildirim, A. Samiei Paghaleh, M. Mirzazadeh, H. Moosaei and A. Biswas, New exact travelling wave solutions for DS-I and DS-II equations,, Nonlinear Analysis: Modelling and Control, 17 (2012), 369.
|
[29] |
E. Zayed and K. A. Gepreel, Some applications of the ${G'}/G$-expansion method to non-linear partial differential equations,, Applied Mathematics and Computation, 212 (2009), 1.
doi: 10.1016/j.amc.2009.02.009. |
[30] |
J. Zhang, F. Jiang and X. Zhao, An improved ${G'}/G$-expansion method for solving nonlinear evolution equations,, International Journal of Computer Mathematics, 87 (2010), 1716.
doi: 10.1080/00207160802450166. |
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