Abstract
This paper mainly studies the bifurcation and single traveling wave solutions of the variable-coefficient Davey–Stewartson system. By employing the traveling wave transformation, the variable-coefficient Davey–Stewartson system is reduced to two-dimensional nonlinear ordinary differential equations. On the one hand, we use the bifurcation theory of planar dynamical systems to draw the phase diagram of the variable-coefficient Davey–Stewartson system. On the other hand, we use the polynomial complete discriminant method to obtain the exact traveling wave solution of the variable-coefficient Davey–Stewartson system.
Highlights
Partial differential equations (PDEs) play a major role in the fields of plasma, quantum mechanics, and engineering [1]
The study of exact traveling wave solutions of nonlinear PDEs with the variable coefficients has always been the focus of mathematicians and physicists, and many experts and scholars [2, 3] have proposed many methods to find PDEs with the variable coefficients, such as variable-coefficient extended mapping method [4], Hirota’s bilinear method [5], Lax integrability [6], and dynamical system approach [7, 8]
We believe that the study of the variable-coefficient Davey–Stewartson system in the paper will help mathematicians and physicists
Summary
Partial differential equations (PDEs) play a major role in the fields of plasma, quantum mechanics, and engineering [1]. In the study of PDEs, the most important thing is to analyze the dynamic behavior and find the exact traveling wave solution. Some exact solutions of equation (1) have been obtained in references [9, 10], the analysis of the dynamic behavior and the classification of traveling wave solutions of this kind of equation have not been reported.
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