title: A generalized simplest equation method and its application to the Boussinesq-Burgers equation.
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.
authors.affiliation: College of Sciences, Inner Mongolia University of Technology, Hohhot, Inner Mongolia, PR China.
authors.forename: Bilige
authors.initials: B
authors.lastname: Sudao
authors.affiliation: College of Sciences, Inner Mongolia University of Technology, Hohhot, Inner Mongolia, PR China.
authors.forename: Xiaomin
authors.initials: X
authors.lastname: Wang
mesh_terms: D000465:Algorithms; D017711:Nonlinear Dynamics