CHINESE JOURNAL OF PHYSICS VOL. 40, NO. 2 APRIL 2002

A New Auto-Bäcklund Transformation and its Applications in Finding Explicit Exact Solutions for the General KdV Equation

Zhenya Yan^*

Department of Applied Mathematics, Dalian University of Technology,

Dalian 116024, China
(Received November 17, 2001)

In this paper, based on a Lax pair of the Riccati form for the general KdV equation, a new auto-Bäcklund transformation (ABT) is presented. As an application of this ABT, since only integration is needed, a series of explicit and exact solutions can be obtained which contain soliton-like solutions. This approach is important for finding more new and physically significant exact solutions of nonlinear evolution equations.

PACS. 03.40.Kf - Waves and wave propagation: general mathematical aspects.

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