2005•Journal of Sichuan Normal UniversityRequires access

The Exact Analytical Solutions to the Burgers-KdV Equation by the Superposition Approach

Hui Liu

Abstract

In this paper, based on the careful analysis of the features of the Burgers equation and the KdV equation as well as the Burgers-KdV equation, the superposition approach which is commonly believed to simplify work for linear partial differential equations is proposed to construct the solutions to the Burgers-KdV equation. Moreover, the exact analytical solutions to the Burgers-KdV equation are successfully derived by means of this method. The results obtained herein are in very good agreement with those given in the existing literature.

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Key concepts: Korteweg–de Vries equation, Burgers' equation, Superposition principle, Partial differential equation, Mathematics, Work (physics), Mathematical analysis, Kadomtsev–Petviashvili equation