Travelling wave solutions of the SchröDinger-Boussinesq system

Abstract

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. © 2012 Adem Klcman and Reza Abazari.