中国物理B ›› 2003, Vol. 12 ›› Issue (3): 245-250.doi: 10.1088/1009-1963/12/3/301

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New applications of the homogeneous balance principle

王跃明1, 王明亮2, 张金良3, 方宗德3   

  1. (1)Department of Mathematics and Physics, Henan University of Science and Technology, Luoyang 471039, China; (2)Department of Mathematics and Physics, Henan University of Science and Technology, Luoyang 471039, China; Department of Mathematics, Lanzhou University, Lanzhou 730000, China; (3)School of Mechanical and Electronic Engineering, Northwestern Polytechnic University, Xi'an 710072, China
  • 收稿日期:2002-07-30 修回日期:2002-12-06 出版日期:2003-03-16 发布日期:2005-03-16
  • 基金资助:
    Project supported by the Natural Science Foundation of Henan Province of China (Grant No 0111050200) and by the Natural Science Foundation of Education Committee of Henan Province of China (Grant No 2000110008).

New applications of the homogeneous balance principle

Zhang Jin-Liang (张金良)a), Wang Yue-Ming (王跃明)b), Wang Ming-Liang (王明亮)b)c), Fang Zong-De (方宗德)a)   

  1. a School of Mechanical and Electronic Engineering, Northwestern Polytechnic University, Xi'an 710072, China; b) Department of Mathematics and Physics, Henan University of Science and Technology, Luoyang 471039, China;  c) Department of Mathematics, Lanzhou 730000, China
  • Received:2002-07-30 Revised:2002-12-06 Online:2003-03-16 Published:2005-03-16
  • Supported by:
    Project supported by the Natural Science Foundation of Henan Province of China (Grant No 0111050200) and by the Natural Science Foundation of Education Committee of Henan Province of China (Grant No 2000110008).

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摘要： The homogeneous balance principle has been widely applied to the exploration of nonlinear transformation, exact solutions (especially solitary wave solution), dromion and similarity reduction to the nonlinear partial differential equations in mathematical physics. In this paper, we use the homogeneous balance principle to derive B?cklund transformations for nonlinear partial differential equations that have more nonlinear terms and more highest-order partial derivative terms. With the aid of the B?cklund transformations derived here, we could obtain exact solutions to the nonlinear partial differential equations. The Davey－Stewartson equation and the Nizhnik－Novikov－Veselov equation are considered as the examples.

关键词: homogeneous balance principle, Davey－Stewartson equation, Nizhnik－Novikov－Veselov equation, Bäcklund transformation, exact solutions

Abstract: The homogeneous balance principle has been widely applied to the exploration of nonlinear transformation, exact solutions (especially solitary wave solution), dromion and similarity reduction to the nonlinear partial differential equations in mathematical physics. In this paper, we use the homogeneous balance principle to derive Bäcklund transformations for nonlinear partial differential equations that have more nonlinear terms and more highest-order partial derivative terms. With the aid of the Bäcklund transformations derived here, we could obtain exact solutions to the nonlinear partial differential equations. The Davey－Stewartson equation and the Nizhnik－Novikov－Veselov equation are considered as the examples.

Key words: homogeneous balance principle, Davey－Stewartson equation, Nizhnik－Novikov－Veselov equation, Bäcklund transformation, exact solutions

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  • 0290