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New soliton solutions for a Kadomtsev-Petviashvili (KP) like equation coupled to a Schrödinger equation. (English) Zbl 1252.35226

Summary: The repeated homogeneous balance is used to construct a new exact traveling wave solution of the Kadomtsev-Petviashvili (KP) like equation coupled to a Schrödinger equation, in which the homogeneous balance method is applied to solve the Riccati equation and the reduced nonlinear ordinary differential equation, respectively. Many new exact traveling wave solutions are successfully obtained, which contain rational and periodic-like solutions. This method is straightforward and concise, and it can be applied to other nonlinear evolution equations.

MSC:

35Q35 PDEs in connection with fluid mechanics
35Q41 Time-dependent Schrödinger equations and Dirac equations
35C08 Soliton solutions
35C07 Traveling wave solutions
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[1] Antonova, Mariana; Biswas, Anjan, Adiabatic parameter dynamics of perturbed solitary waves, Commun. Nonlinear Sci. Numer. Simulat., 14, 734-748 (2009) · Zbl 1221.35321
[2] Fan, E. G.; Zhang, H. Q., A note on the homogeneous balance method, Phys. Lett. A, 246, 403-406 (1998) · Zbl 1125.35308
[3] Fan, E. G., Auto-Bäcklund transformation and similarity reductions for general variable coefficient KdV equations, Phys. Lett. A, 294, 26-30 (2002) · Zbl 0981.35064
[4] Wang, M. L.; Wang, Y. M., A new Bäcklund transformation and multi-soliton solutions to the KdV equation with general variable coefficients, Phys. Lett. A, 287, 211-216 (2001) · Zbl 0971.35064
[5] Wang, M. L., Solitary wave solution for variant Boussinesq equations, Phys. Lett. A, 199, 169-172 (1995) · Zbl 1020.35528
[6] Wang, M. L., Application of homogeneous balance method to exact solutions of nonlinear equation in mathematical physics, Phys. Lett. A, 216, 67-75 (1996) · Zbl 1125.35401
[7] Wang, M. L.; Zhou, Y. B.; Li, Z. B., Application of a homogeneous balance method to exact solutions of nonlinear equations in mathematical physics, Phys. Lett. A, 216, 67-75 (1996) · Zbl 1125.35401
[8] Khalfallah, Mohammed, New exact traveling wave solutions of the (3+1) dimensional Kadomtsev-Petviashvili (KP) equation, Commun. Nonlinear Sci. Numer. Simulat., 14, 1169-1175 (2009) · Zbl 1221.35341
[9] Khalfallah, Mohammed, Exact traveling wave solutions of the Boussinesq-Burgers equation, Math. Comput. Model., 49, 666-671 (2009) · Zbl 1165.35445
[10] Abdel Rady, A. S.; Khater, A. H.; Osman, E. S.; Khalfallah, Mohammed, New periodic wave and soliton solutions for system of coupled Korteweg-de Vries equations, Appl. Math. Comput., 207, 406414 (2009) · Zbl 1159.35406
[11] Abdel Rady, A. S.; Osman, E. S.; Khalfallah, Mohammed, “Multi soliton solution for the system of coupled Korteweg-de Vries equations”, Appl. Math. Comput., 210, 177-181 (2009) · Zbl 1163.35467
[12] Abdel Rady, A. S.; Osman, E. S.; Khalfallah, Mohammed, On soliton solutions for a generalized Hirota-Satsuma coupled KdV equation, Commun. Nonlinear Sci. Numer. Simulat., 15, 264-274 (2010) · Zbl 1221.35358
[13] Abdel Rady, A. S.; Khalfallah, Mohammed, On soliton solutions for Boussinesq-Burgers equations, Commun. Nonlinear Sci. Numer. Simulat., 15, 886-894 (2010) · Zbl 1221.35357
[14] Abdel Rady, A. S.; Osman, E. S.; Khalfallah, Mohammed; solution, Multi soliton, rational solution of the Boussinesq-Burgers equations, Commun. Nonlinear Sci. Numer. Simulat., 15, 1172-1176 (2010) · Zbl 1221.35359
[15] Fan, E. G., Two new applications of the homogeneous balance method, Phys. Lett. A, 265, 353-357 (2000) · Zbl 0947.35012
[16] Ma, W. X.; Fuchssteiner, B., Explicit and exact solutions to a Kolmogorov-Petrovskii-Piskunov equation, Int. J. Nonlinear Mech., 31, 329-338 (1996) · Zbl 0863.35106
[17] Bai, C. L., Exact solutions for nonlinear partial differential equation: a new approach, Phys. Lett. A, 288, 191-195 (2001) · Zbl 0970.35002
[18] Bai, C. L.; Zhao, Hong, Complex hyperbolic-function method and its applications to nonlinear equations, Phys. Lett. A, 355, 32-38 (2006)
[19] Bai, C. L., A new generalization of variable coefficients algebraic method for solving nonlinear evolution equations, Chaos Soliton Fract., 34, 1114-1129 (2007) · Zbl 1142.35562
[20] Zhao, Hong, Applications of the generalized algebraic method to special-type nonlinear equations, Chaos Soliton Fract., 36, 359-369 (2008) · Zbl 1132.65099
[21] Hu, X. B., The higher-order KdV equation with a source and nonlinear superposition formula, Chaos Soliton Fract., 7, 211-215 (1996) · Zbl 1080.35535
[22] Zhao, X. Q.; Tang, D. B., A new note on a homogeneous balance method, Phys. Lett. A, 297, 59-67 (2002) · Zbl 0994.35005
[23] Zhu, Shun-dong, The generalizing Riccati equation mapping method in non-linear evolution equation: application to (2+1)-dimensional BoitiLeonPempinelle equation, Chaos Soliton Fract., 37, 1335-1342 (2008) · Zbl 1142.35597
[24] Fan, E. G., Soliton solutions for a generalized Hirota Satsuma coupled KdV equation and a coupled MKdV equation, Phys. Lett. A, 282, 18-22 (2001) · Zbl 0984.37092
[25] Bai, C. L.; Zhuo, H., Generalized extended tanh-function method and its application, Chaos Soliton Fract., 27, 1026-1035 (2006) · Zbl 1088.35534
[26] Bai, C. L., Multiple soliton solutions of the high order Broer-Kaup equations, Commun. Theor. Phys., 34, 729-732 (2000)
[27] Bai, C. L., Abundant multi-soliton structure of the (3+1)-dimensional Nizhnik-Novikov-Veselov equations, Commun. Theor. Phys., 41, 15-20 (2004) · Zbl 1167.35453
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