Exact solutions of travelling wave model via dynamical system method. (English) Zbl 1470.35341

Summary: By using the method of dynamical system, the exact travelling wave solutions of the coupled nonlinear Schrödinger-Boussinesq equations are studied. Based on this method, the bounded exact travelling wave solutions are obtained which contain solitary wave solutions and periodic travelling wave solutions. The solitary wave solutions and periodic travelling wave solutions are expressed by the hyperbolic functions and the Jacobian elliptic functions, respectively. The results show that the presented findings improve the related previous conclusions. Furthermore, the numerical simulations of the solitary wave solutions and the periodic travelling wave solutions are given to show the correctness of our results.


35Q55 NLS equations (nonlinear Schrödinger equations)
35C07 Traveling wave solutions
35Q53 KdV equations (Korteweg-de Vries equations)
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