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The investigation of solutions to the coupled Schrödinger-Boussinesq equations. (English) Zbl 1297.35013

Summary: The \((G'/G)\)-expansion method and the symbolic computation system Mathematica are employed to investigate the coupled Schrödinger-Boussinesq equations. The hyperbolic function solutions, trigonometric function solutions, and rational function solutions to the equations are obtained. The decaying properties of several solutions are analyzed.

MSC:

35A35 Theoretical approximation in context of PDEs
35Q55 NLS equations (nonlinear Schrödinger equations)

Software:

Mathematica
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References:

[1] Guo, B. L.; Shen, L. J., The global solution of initial value problem for nonlinear Schrödinger-Boussinesq equation in 3-dimensions, Acta Mathematicae Applicatae Sinica, 6, 1, 11-21, (1990) · Zbl 0705.35129
[2] Guo, B.; Du, X., Existence of the periodic solution for the weakly damped Schrödinger-Boussinesq equation, Journal of Mathematical Analysis and Applications, 262, 2, 453-472, (2001) · Zbl 1040.35114
[3] Kılıcman, A.; Abazari, R., Travelling wave solutions of the Schrödinger-Boussinesq system, Abstract and Applied Analysis, 2012, (2012) · Zbl 1253.65162
[4] Lai, S. Y.; Wiwatanapataphe, B., The asymptotics of global solutions for semilinear wave equations in two space dimensions, Dynamics of Continuous, Discrete & Impulsive Systems. Series B, 18, 5, 647-657, (2011) · Zbl 1270.35319
[5] Lai, S.; Wu, Y. H.; Wiwatanapataphee, B., On exact travelling wave solutions for two types of nonlinear \(####\) equations and a generalized KP equation, Journal of Computational and Applied Mathematics, 212, 2, 291-299, (2008) · Zbl 1187.35216
[6] Lai, S.; Wu, Y., The local well-posedness and existence of weak solutions for a generalized Camassa-Holm equation, Journal of Differential Equations, 248, 8, 2038-2063, (2010) · Zbl 1187.35179
[7] Lai, S.; Wang, A., The well-posedness of solutions for a generalized shallow water wave equation, Abstract and Applied Analysis, 2012, (2012) · Zbl 1242.35191
[8] Schamel, H.; Elsässer, K., The application of the spectral method to nonlinear wave propagation, Journal of Computational Physics, 22, 4, 501-516, (1976) · Zbl 0344.65055
[9] Makhankov, V. G., On stationary solutions of Schrödinger equation with a self-consistent potential satisfying Boussinesq’s equations, Physics Letters A, 50, 1, 42-44, (1974)
[10] Chen, H. L.; Xu, Z. H., Periodic wave solutions for the coupled Schrödinger-Boussinesq equations, Acta Mathematicae Applicatae Sinica, 29, 5, 955-960, (2006)
[11] Cai, G. L.; Zhang, F. Y.; Ren, L., More exact solutions for coupling Schrödinger-Boussinesq equations by a modified F-expansion method, Mathematica Applicata, 21, 1, 90-97, (2008) · Zbl 1164.35488
[12] Wang, M.; Li, X.; Zhang, J., The \((G^\prime / G)\)-expansion method and travelling wave solutions of nonlinear evolution equations in mathematical physics, Physics Letters A, 372, 4, 417-423, (2008) · Zbl 1217.76023
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