Travelling Wave Solutions of the Schrödinger-Boussinesq System

We establish exact solutions for the Schrödinger-Boussinesq System iut+uxx−auv=0, vtt−vxx+vxxxx−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.