Travelling wave solutions of the Schrödinger-Boussinesq system. (English) Zbl 1253.65162

Summary: We establish exact solutions for the Schrödinger-Boussinesq system \(iu_t + u_{xx} - auv = 0, v_{tt} - v_{xx} + v_{xxxx} - b(|u|^2)_{xx} = 0\), where \(a\) and \(b\) are real constants. The \((G'/G)\)-expansion method is used to construct exact periodic and soliton solutions of this equation. Our work is motivated by the fact that the \((G'/G)\)-expansion method provides not only more general forms of solutions but also periodic and solitary waves. As a result, hyperbolic function solutions and trigonometric function solutions with parameters are obtained. These solutions may be important and of significance for the explanation of some practical physical problems.


65M99 Numerical methods for partial differential equations, initial value and time-dependent initial-boundary value problems
35Q53 KdV equations (Korteweg-de Vries equations)
Full Text: DOI


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