Elsevier

Physics Letters A

Volume 291, Issue 6, 17 December 2001, Pages 376-380
Physics Letters A

A new complex line soliton for the two-dimensional KdV–Burgers equation

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Abstract

Making use of a extended tanh method with symbolic computation, we find a new complex line soliton for the two-dimensional (2D) KdV–Burgers equation. Its real part is the sum of the shock wave solution of a 2D Burgers equation and the solitary wave solution of a 2D KdV (KP) equation, and its imaginary part is the product of the shock wave solution of a 2D Burgers equation and the solitary wave solution of a 2D MKdV (MKP) equation.

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Acknowledgements

The first author is grateful to Professor Gu Chaohao, Professor Hu Hesheng and Professor Zhou Zixiang for their enthusiastic guidance and help. We would like express our sincere thanks to the referees for their useful suggestion. This work has been supported by Chinese Basic Research Plan “Mathematics Mechanization and a Platform for Automated Reasoning”, the Postdoctoral Science Foundation of China and the City University strategic research grant 7001209.

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