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.


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


Full Text: DOI


[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
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.