中国物理B ›› 1998, Vol. 7 ›› Issue (9): 649-654.doi: 10.1088/1004-423X/7/9/002

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B?CKLUND TRANSFORMATION, LAX PAIRS, SYMMETRIES AND EXACT SOLUTIONS FOR VARIABLE COEFFICIENT KdV EQUATION

张鸿庆1, 范恩贵2, 林钢3   

  1. (1)Institute of Mathematics, Dalian University of Technology, Dalian 116024, China; (2)Institute of Mathematics, Dalian University of Technology, Dalian 116024, China; State Key Laboratory of Coastal and Offshore Engineering, Dalian University of Technology, Dalian 116024, China; (3)State Key Laboratory of Coastal and Offshore Engineering, Dalian University of Technology, Dalian 116024, China
  • 收稿日期:1998-03-09 修回日期:1998-05-03 出版日期:1998-09-20 发布日期:1998-09-20
  • 基金资助:
    Project supported by the National Natural Science Foundation of China under the Grant No. 19572022.

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   

  1. 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
  • Received:1998-03-09 Revised:1998-05-03 Online:1998-09-20 Published:1998-09-20
  • Supported by:
    Project supported by the National Natural Science Foundation of China under the Grant No. 19572022.

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摘要： The homogeneous balance method is extended to seek for B?cklund transformation, Lax pairs, non-local symmetries of variable coefficient KdV equation (VCKdVE). Then based on the B?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.

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.

中图分类号:  (Solitons)

  • 05.45.Yv
02.30.Hq (Ordinary differential equations) 02.30.Jr (Partial differential equations)