A Generalized Simplest Equation Method and Its Application to the Boussinesq-Burgers Equation |
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| Authors: | Bilige Sudao Xiaomin Wang |
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| Institution: | College of Sciences, Inner Mongolia University of Technology, Hohhot, Inner Mongolia, PR China.; Centro de Investigacion Cientifica y Educacion Superior de Ensenada, MEXICO, |
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| Abstract: | In this paper, a generalized simplest equation method is proposed to seek exact solutions of nonlinear evolution equations (NLEEs). In the method, we chose a solution expression with a variable coefficient and a variable coefficient ordinary differential auxiliary equation. This method can yield a Bäcklund transformation between NLEEs and a related constraint equation. By dealing with the constraint equation, we can derive infinite number of exact solutions for NLEEs. These solutions include the traveling wave solutions, non-traveling wave solutions, multi-soliton solutions, rational solutions, and other types of solutions. As applications, we obtained wide classes of exact solutions for the Boussinesq-Burgers equation by using the generalized simplest equation method. |
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