New applications of the homogeneous balance principle |
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Authors: | Zhang Jin-Liang Wang Yue-Ming Wang Ming-Liang and Fang Zong-De |
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Institution: | School of Mechanical and Electronic Engineering, Northwestern Polytechnic University, Xi'an 710072, China; Department of Mathematics and Physics, Henan University of Science and Technology, Luoyang 471039, China; Department of Mathematics, Lanzhou 730000, China |
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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. |
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Keywords: | homogeneous balance principle Davey-Stewartson equation Nizhnik-Novikov-Veselov equation Bäcklund transformation exact solutions |
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