B?CKLUND TRANSFORMATION, LAX PAIRS, SYMMETRIES AND EXACT SOLUTIONS FOR VARIABLE COEFFICIENT KdV EQUATION
Fan En-gui (范恩贵)ab, Zhang Hong-qing (张鸿庆)a, Lin Gang (林钢)b
a Institute of Mathematics, Dalian University of Technology, Dalian 116024, China; b State Key Laboratory of Coastal and Offshore Engineering, Dalian University of Technology, Dalian 116024, China
Abstract The homogeneous balance method is extended to seek for B$\ddot{\rm a}$cklund transformation, Lax pairs, non-local symmetries of variable coefficient KdV equation (VCKdVE). Then based on the B$\ddot{\rm a}$cklund transformation and general solutions of a fourth-order nonlinear ordinary differential equation, five kinds of exact solutions of VCKdVE are derived. The soliton-like solution also belongs to these solutions.
Received: 09 March 1998
Revised: 03 May 1998
Accepted manuscript online:
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