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)
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
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.
Received: 30 July 2002
Revised: 06 December 2002
Accepted manuscript online:
Fund: 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).
Cite this article:
Zhang Jin-Liang (张金良), Wang Yue-Ming (王跃明), Wang Ming-Liang (王明亮), Fang Zong-De (方宗德) New applications of the homogeneous balance principle 2003 Chinese Physics 12 245
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