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Complex spatiotemporal behavior in a chain of one-way nonlinearly coupled elements
Bose-Einstein condensates and spectral properties of multicomponent nonlinear Schrödinger equations
1. | Institute for Nuclear Research and Nuclear Energy, Bulgarian academy of sciences, 72 Tsarigradsko chaussee, 1784 Sofia, Bulgaria |
References:
[1] |
M. J. Ablowitz, B. Prinari and A. D. Trubatch, "Discrete and Continuous Nonlinear Schrödinger Systems,", London Mathematical Society Lecture Note Series, (2004).
|
[2] |
E. V. Doktorov, J. Wang and J. Yang, Perturbation theory for bright spinor Bose-Einstein condensate solitons,, Phys. Rev. A, 77 (2008).
doi: 10.1103/PhysRevA.77.043617. |
[3] |
L. D. Faddeev and L. A. Takhtadjan, "Hamiltonian Approach in the Theory of Solitons,", Springer Verlag, (1987). Google Scholar |
[4] |
A. P. Fordy and P. P. Kulish, Nonlinear Schrodinger equations and simple Lie algebras,, Commun. Math. Phys., 89 (1983), 427.
doi: 10.1007/BF01214664. |
[5] |
V. S. Gerdjikov, Generalised Fourier transforms for the soliton equations. Gauge covariant formulation,, Inverse Problems, 2 (1986), 51.
doi: 10.1088/0266-5611/2/1/005. |
[6] |
V. S. Gerdjikov, The Zakharov-Shabat dressing method and the representation theory of the semisimple Lie algebras,, Phys. Lett. A, 126 (1987), 184.
doi: 10.1016/0375-9601(87)90457-9. |
[7] |
V. S. Gerdjikov, The generalized Zakharov-Shabat system and the soliton perturbations,, Theor. Math. Phys., 99 (1994), 292.
doi: 10.1007/BF01016144. |
[8] |
V. S. Gerdjikov, On reductions of soliton solutions of multi-component NLS models and spinor Bose-Einstein condensates,, Application of mathematics in technical and natural sciences, (1186), 15.
|
[9] |
V. S. Gerdjikov, G. G. Grahovski and N. A. Kostov, Multicomponent equations of the nonlinear Schrödinger type on symmetric spaces and their reductions,, (Russian) Teoret. Mat. Fiz., 144 (2005), 313.
|
[10] |
V. S. Gerdjikov, D. J. Kaup, N. A. Kostov and T. I. Valchev, On classification of soliton solutions of multicomponent nonlinear evolution equations,, J. Phys. A: Math. Theor., 41 (2008).
doi: 10.1088/1751-8113/41/31/315213. |
[11] |
V. S. Gerdjikov, N. A. Kostov and T. I. Valchev, Bose-Einstein condensates with $F=1$ and $F=2$. Reductions and soliton interactions of multi-component NLS models,, in, 7501 (2009). Google Scholar |
[12] |
V. S. Gerdjikov, N. A. Kostov and T. I. Valchev, Solutions of multi-component NLS models and spinor Bose-Einstein condensates,, Physica D, 238 (2009), 1306.
doi: 10.1016/j.physd.2008.06.007. |
[13] |
S. Helgasson, "Differential Geometry, Lie groups and Symmetric Spaces,", Academic Press, (1978). Google Scholar |
[14] |
J. Ieda, T. Miyakawa and M. Wadati, Exact analysis of soliton dynamics in spinor Bose-Einstein condensates,, Phys. Rev Lett., 93 (2004).
doi: 10.1103/PhysRevLett.93.194102. |
[15] |
J. Ieda, T. Miyakawa and M. Wadati, Matter-wave solitons in an $F=1$ spinor Bose-Einstein condensate,, J. Phys. Soc. Jpn., 73 (2004).
doi: 10.1143/JPSJ.73.2996. |
[16] |
T. Kanna and M. Lakshmanan, Exact soliton solutions of coupled nonlinear Schrödinger equations: Shape-changing collisions, logic gates, and partially coherent solitons,, Phys. Rev. E, 67 (2003).
doi: 10.1103/PhysRevE.67.046617. |
[17] |
N. A. Kostov, V. A. Atanasov, V. S. Gerdjikov and G. G. Grahovski, On the soliton solutions of the spinor Bose-Einstein condensate,, Proceedings of SPIE, 6604 (2007).
doi: 10.1117/12.727191. |
[18] |
N. A. Kostov and V. S. Gerdjikov, Reductions of multicomponent mKdV equations on symmetric spaces of DIII-type,, SIGMA, 4 (2008). Google Scholar |
[19] |
L. Li, Z. Li, B. A. Malomed, D. Mihalache and W. M. Liu, Exact soliton solutions and nonlinear modulation instability in spinor Bose-Einstein condensates,, Phys. Rev. A, 72 (2005).
doi: 10.1103/PhysRevA.72.033611. |
[20] |
S. V. Manakov, On the theory of two-dimensional stationary self-focusing of electromagnetic waves,, Zh. Eksp. Teor. Fiz, 65 (1973), 505. Google Scholar |
[21] |
A. V. Mikhailov, The reduction problem and the inverse scattering method,, Physica D: Nonlinear Phenomena, 3 (1981), 73.
doi: 10.1016/0167-2789(81)90120-2. |
[22] |
H. E. Nistazakis, D. J. Frantzeskakis, P. G. Kevrekidis, B. A. Malomed and R. Carretero-Gonzalez, Bright-dark soliton complexes in spinor Bose-Einstein condensates,, Phys. Rev. A, 77 (2008).
doi: 10.1103/PhysRevA.77.033612. |
[23] |
Q.-H. Park and H. J. Shin, Painlevé analysis of the coupled nonlinear Schrödinger equation for polarized optical waves in an isotropic medium,, Phys. Rev. E, 59 (1999), 2373.
doi: 10.1103/PhysRevE.59.2373. |
[24] |
M. Salerno, Matter-wave quantum dots and antidots in ultracold atomic Bose-Fermi mixtures,, Phys. Rev. A, 72 (2005). Google Scholar |
[25] |
T. Tsuchida, N-soliton collision in the Manakov model,, Prog. Theor. Phys., 111 (2004), 151.
doi: 10.1143/PTP.111.151. |
[26] |
T. Tsuchida and M. Wadati, The coupled modified Korteweg-de Vries equations,, J. Phys. Soc. Jpn., 67 (1998).
doi: 10.1143/JPSJ.67.1175. |
[27] |
M. Uchiyama, J. Ieda and M. Wadati, Dark solitons in $F=1$ spinor Bose-Einstein condensate,, J. Phys. Soc. Jpn., 75 (2006).
doi: 10.1143/JPSJ.75.064002. |
[28] |
M. Uchiyama, J. Ieda and M. Wadati, Multicomponent bright solitons in $F=2$ spinor Bose-Einstein condensates,, J. Phys. Soc. Japan, 76 (2007).
doi: 10.1143/JPSJ.76.074005. |
[29] |
V. E. Zakharov, S. V. Manakov, S. P. Novikov and L. I. Pitaevskii, "Theory of Solitons. The Inverse Scattering Method,", Plenum, (1984). Google Scholar |
[30] |
V. E. Zakharov and A. V. Mikhailov, On the integrability of classical spinor models in two-dimensional space-time,, Comm. Math. Phys., 74 (1980), 21.
doi: 10.1007/BF01197576. |
[31] |
V. E. Zakharov and A. B. Shabat, Exact theory of two-dimensional self-focusing and one-dimensional self-modulation of waves in nonlinear media,, Soviet Physics-JETP, 34 (1972), 62. Google Scholar |
[32] |
V. E. Zakharov and A. B. Shabat, A scheme for integrating the nonlinear equations of mathematical physics by the method of the inverse scattering problem. I.,, Functional Analysis and Its Applications, 8 (1974), 226.
doi: 10.1007/BF01075696. |
[33] |
V. E. Zakharov and A. B. Shabat, Integration of nonlinear equations of mathematical physics by the method of inverse scattering. II.,, Functional Analysis and Its Applications, 13 (1974), 166. Google Scholar |
show all references
References:
[1] |
M. J. Ablowitz, B. Prinari and A. D. Trubatch, "Discrete and Continuous Nonlinear Schrödinger Systems,", London Mathematical Society Lecture Note Series, (2004).
|
[2] |
E. V. Doktorov, J. Wang and J. Yang, Perturbation theory for bright spinor Bose-Einstein condensate solitons,, Phys. Rev. A, 77 (2008).
doi: 10.1103/PhysRevA.77.043617. |
[3] |
L. D. Faddeev and L. A. Takhtadjan, "Hamiltonian Approach in the Theory of Solitons,", Springer Verlag, (1987). Google Scholar |
[4] |
A. P. Fordy and P. P. Kulish, Nonlinear Schrodinger equations and simple Lie algebras,, Commun. Math. Phys., 89 (1983), 427.
doi: 10.1007/BF01214664. |
[5] |
V. S. Gerdjikov, Generalised Fourier transforms for the soliton equations. Gauge covariant formulation,, Inverse Problems, 2 (1986), 51.
doi: 10.1088/0266-5611/2/1/005. |
[6] |
V. S. Gerdjikov, The Zakharov-Shabat dressing method and the representation theory of the semisimple Lie algebras,, Phys. Lett. A, 126 (1987), 184.
doi: 10.1016/0375-9601(87)90457-9. |
[7] |
V. S. Gerdjikov, The generalized Zakharov-Shabat system and the soliton perturbations,, Theor. Math. Phys., 99 (1994), 292.
doi: 10.1007/BF01016144. |
[8] |
V. S. Gerdjikov, On reductions of soliton solutions of multi-component NLS models and spinor Bose-Einstein condensates,, Application of mathematics in technical and natural sciences, (1186), 15.
|
[9] |
V. S. Gerdjikov, G. G. Grahovski and N. A. Kostov, Multicomponent equations of the nonlinear Schrödinger type on symmetric spaces and their reductions,, (Russian) Teoret. Mat. Fiz., 144 (2005), 313.
|
[10] |
V. S. Gerdjikov, D. J. Kaup, N. A. Kostov and T. I. Valchev, On classification of soliton solutions of multicomponent nonlinear evolution equations,, J. Phys. A: Math. Theor., 41 (2008).
doi: 10.1088/1751-8113/41/31/315213. |
[11] |
V. S. Gerdjikov, N. A. Kostov and T. I. Valchev, Bose-Einstein condensates with $F=1$ and $F=2$. Reductions and soliton interactions of multi-component NLS models,, in, 7501 (2009). Google Scholar |
[12] |
V. S. Gerdjikov, N. A. Kostov and T. I. Valchev, Solutions of multi-component NLS models and spinor Bose-Einstein condensates,, Physica D, 238 (2009), 1306.
doi: 10.1016/j.physd.2008.06.007. |
[13] |
S. Helgasson, "Differential Geometry, Lie groups and Symmetric Spaces,", Academic Press, (1978). Google Scholar |
[14] |
J. Ieda, T. Miyakawa and M. Wadati, Exact analysis of soliton dynamics in spinor Bose-Einstein condensates,, Phys. Rev Lett., 93 (2004).
doi: 10.1103/PhysRevLett.93.194102. |
[15] |
J. Ieda, T. Miyakawa and M. Wadati, Matter-wave solitons in an $F=1$ spinor Bose-Einstein condensate,, J. Phys. Soc. Jpn., 73 (2004).
doi: 10.1143/JPSJ.73.2996. |
[16] |
T. Kanna and M. Lakshmanan, Exact soliton solutions of coupled nonlinear Schrödinger equations: Shape-changing collisions, logic gates, and partially coherent solitons,, Phys. Rev. E, 67 (2003).
doi: 10.1103/PhysRevE.67.046617. |
[17] |
N. A. Kostov, V. A. Atanasov, V. S. Gerdjikov and G. G. Grahovski, On the soliton solutions of the spinor Bose-Einstein condensate,, Proceedings of SPIE, 6604 (2007).
doi: 10.1117/12.727191. |
[18] |
N. A. Kostov and V. S. Gerdjikov, Reductions of multicomponent mKdV equations on symmetric spaces of DIII-type,, SIGMA, 4 (2008). Google Scholar |
[19] |
L. Li, Z. Li, B. A. Malomed, D. Mihalache and W. M. Liu, Exact soliton solutions and nonlinear modulation instability in spinor Bose-Einstein condensates,, Phys. Rev. A, 72 (2005).
doi: 10.1103/PhysRevA.72.033611. |
[20] |
S. V. Manakov, On the theory of two-dimensional stationary self-focusing of electromagnetic waves,, Zh. Eksp. Teor. Fiz, 65 (1973), 505. Google Scholar |
[21] |
A. V. Mikhailov, The reduction problem and the inverse scattering method,, Physica D: Nonlinear Phenomena, 3 (1981), 73.
doi: 10.1016/0167-2789(81)90120-2. |
[22] |
H. E. Nistazakis, D. J. Frantzeskakis, P. G. Kevrekidis, B. A. Malomed and R. Carretero-Gonzalez, Bright-dark soliton complexes in spinor Bose-Einstein condensates,, Phys. Rev. A, 77 (2008).
doi: 10.1103/PhysRevA.77.033612. |
[23] |
Q.-H. Park and H. J. Shin, Painlevé analysis of the coupled nonlinear Schrödinger equation for polarized optical waves in an isotropic medium,, Phys. Rev. E, 59 (1999), 2373.
doi: 10.1103/PhysRevE.59.2373. |
[24] |
M. Salerno, Matter-wave quantum dots and antidots in ultracold atomic Bose-Fermi mixtures,, Phys. Rev. A, 72 (2005). Google Scholar |
[25] |
T. Tsuchida, N-soliton collision in the Manakov model,, Prog. Theor. Phys., 111 (2004), 151.
doi: 10.1143/PTP.111.151. |
[26] |
T. Tsuchida and M. Wadati, The coupled modified Korteweg-de Vries equations,, J. Phys. Soc. Jpn., 67 (1998).
doi: 10.1143/JPSJ.67.1175. |
[27] |
M. Uchiyama, J. Ieda and M. Wadati, Dark solitons in $F=1$ spinor Bose-Einstein condensate,, J. Phys. Soc. Jpn., 75 (2006).
doi: 10.1143/JPSJ.75.064002. |
[28] |
M. Uchiyama, J. Ieda and M. Wadati, Multicomponent bright solitons in $F=2$ spinor Bose-Einstein condensates,, J. Phys. Soc. Japan, 76 (2007).
doi: 10.1143/JPSJ.76.074005. |
[29] |
V. E. Zakharov, S. V. Manakov, S. P. Novikov and L. I. Pitaevskii, "Theory of Solitons. The Inverse Scattering Method,", Plenum, (1984). Google Scholar |
[30] |
V. E. Zakharov and A. V. Mikhailov, On the integrability of classical spinor models in two-dimensional space-time,, Comm. Math. Phys., 74 (1980), 21.
doi: 10.1007/BF01197576. |
[31] |
V. E. Zakharov and A. B. Shabat, Exact theory of two-dimensional self-focusing and one-dimensional self-modulation of waves in nonlinear media,, Soviet Physics-JETP, 34 (1972), 62. Google Scholar |
[32] |
V. E. Zakharov and A. B. Shabat, A scheme for integrating the nonlinear equations of mathematical physics by the method of the inverse scattering problem. I.,, Functional Analysis and Its Applications, 8 (1974), 226.
doi: 10.1007/BF01075696. |
[33] |
V. E. Zakharov and A. B. Shabat, Integration of nonlinear equations of mathematical physics by the method of inverse scattering. II.,, Functional Analysis and Its Applications, 13 (1974), 166. Google Scholar |
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