Classification of multiply travelling wave solutions for coupled Burgers, combined KdV-modified KdV, and Schrödinger-KdV equations. (English) Zbl 1356.35208

Summary: Some explicit travelling wave solutions to constructing exact solutions of nonlinear partial differential equations of mathematical physics are presented. By applying a theory of Frobenius decompositions and, more precisely, by using a transformation method to the coupled Burgers, combined Korteweg-de Vries- (KdV-) modified KdV and Schrödinger-KdV equation is written as bilinear ordinary differential equations and two solutions to describing nonlinear interaction of travelling waves are generated. The properties of the multiple travelling wave solutions are shown by some figures. All solutions are stable and have applications in physics.


35Q53 KdV equations (Korteweg-de Vries equations)
35C07 Traveling wave solutions
35Q55 NLS equations (nonlinear Schrödinger equations)
34L40 Particular ordinary differential operators (Dirac, one-dimensional Schrödinger, etc.)
35B35 Stability in context of PDEs
Full Text: DOI


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