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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.

MSC:

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