A Generalized Simplest Equation Method and Its Application to the Boussinesq-Burgers Equation

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 B...

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Detalles Bibliográficos
Autores principales: Sudao, Bilige, Wang, Xiaomin
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Public Library of Science 2015
Materias:
Research Article
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4431887/
https://www.ncbi.nlm.nih.gov/pubmed/25973605
http://dx.doi.org/10.1371/journal.pone.0126635
Descripción
Sumario: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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