Traveling waves to a Burgers-Korteweg-de Vries-type equation with higher-order nonlinearities |
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| Authors: | Zhaosheng Feng Roger Knobel |
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| Institution: | a Department of Mathematics, University of Texas-Pan American, Edinburg, TX 78541, USA
b Department of Mathematics, Tianjin University of Technology and Education, Tianjing 300222, China |
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| Abstract: | In this paper, first we survey some recent advances in the study of traveling wave solutions to the Burgers-Korteweg-de Vries equation and some comments are given. Then, we study a Burgers-Korteweg-de Vries-type equation with higher-order nonlinearities. A qualitative analysis to a two-dimensional autonomous system which is equivalent to the Burgers-KdV-type equation is presented, and indicates that under certain conditions, the Burgers-Korteweg-de Vries-type equation has neither nontrivial bell-profile solitary waves, nor periodic waves. Finally, a solitary wave solution is obtained by means of the first-integral method which is based on the ring theory of commutative algebra. |
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| Keywords: | Solitary wave First integral Autonomous system Burgers-KdV equation Bendixson theorem Painlevé analysis |
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