The Korteweg–de Vries–Burgers equation and its approximate solution

Abstract

In this paper, we study the Korteweg–de Vries–Burgers equation with boundary conditions. After making a series of transformations, we convert the Korteweg–de Vries–Burgers equation into an Emden–Fowler equation. An approximate solution in series form is obtained by means of the Adomian decomposition method. The solution is illustrated to agree well with phase plane analysis.

Keywords:

• Travelling wave
• Korteweg–de Vries–Burgers equation
• Approximate solution
• Decomposition method
• Shock-profile wave

AMS Subject Classification :

• 34E05
• 35Q53
• 41A30

Acknowledgements

The work is supported by UTPA Faculty Research Council Grant 119100 and partly supported by NSF Grant CCF–0514768. Part of the content was presented at the Sixth AIMS International Conference on Dynamical Systems, Differential Equations and Applications, University of Poitiers, France, 25–28 June 2006 (http://aimsciences.org /AIMS-Conference/2006/).