中国物理B ›› 2002, Vol. 11 ›› Issue (7): 651-655.doi: 10.1088/1009-1963/11/7/301

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B?cklund transformation and variable separation solutions for the generalized Nozhnik-Novikov-Veselov equation

张解放   

  1. Institute of Nonlinear Physics , Zhejiang Normal University, Jinhua 321004, China; Shanghai Institute of Applied Mathematics and Mechanics, Shanghai University, Shanghai 200072 China
  • 收稿日期:2001-12-04 修回日期:2002-03-28 出版日期:2002-07-12 发布日期:2005-06-12
  • 基金资助:
    Project supported by the Natural Science Foundation of Zhejiang Province, China (Grant No 100039).

Bäcklund transformation and variable separation solutions for the generalized Nozhnik-Novikov-Veselov equation

Zhang Jie-Fang (张解放)   

  1. Institute of Nonlinear Physics , Zhejiang Normal University, Jinhua 321004, China; Shanghai Institute of Applied Mathematics and Mechanics, Shanghai University, Shanghai 200072 China
  • Received:2001-12-04 Revised:2002-03-28 Online:2002-07-12 Published:2005-06-12
  • Supported by:
    Project supported by the Natural Science Foundation of Zhejiang Province, China (Grant No 100039).

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摘要： Using the extended homogeneous balance method, the B?cklund transformation for a (2+1)-dimensional integrable model, the generalized Nizhnik－Novikov－Veselov (GNNV) equation, is first obtained. Also, making use of the B?cklund transformation, the GNNV equation is changed into three equations: linear, bilinear and trilinear form equations. Starting from these three equations, a rather general variable separation solution of the model is constructed. The abundant localized coherent structures of the model can be induced by the entrance of two variable-separated arbitrary functions.

Abstract: Using the extended homogeneous balance method, the B?cklund transformation for a (2+1)-dimensional integrable model, the generalized Nizhnik－Novikov－Veselov (GNNV) equation, is first obtained. Also, making use of the B?cklund transformation, the GNNV equation is changed into three equations: linear, bilinear and trilinear form equations. Starting from these three equations, a rather general variable separation solution of the model is constructed. The abundant localized coherent structures of the model can be induced by the entrance of two variable-separated arbitrary functions.

Key words: extended homogeneous balance method, (2+1) dimensions, GNNV equation, localized coherent structures

中图分类号:  (Ordinary differential equations)

  • 02.30.Hq
02.60.Lj (Ordinary and partial differential equations; boundary value problems) 02.30.Fn (Several complex variables and analytic spaces)