2017•Journal of Applied Mathematics and PhysicsOpen access

Application of the Generalized Simplest Equation Method to the Burgers Equation

Yuexing Bai, Sudao Bilige, Xiaoqing Gao, Jianqing Lü

Abstract

We successfully constructed wide classes of exact solutions for the Burgers equation by using the generalized simplest equation method. This method yielded a Bäcklund transformation between the Burgers equation and a related constraint equation. By dealing with the constraint equation, we obtained the traveling wave solutions and non-traveling wave solutions of the Burgers equation.

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Key concepts: Burgers' equation, Kadomtsev–Petviashvili equation, Mathematics, Fisher's equation, Transformation (genetics), Constraint (computer-aided design), Exact differential equation, Riccati equation