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一个非线性扩散方程的PAINLEVE-BEACKLUND变换及其精确解 被引量:1

The Painlevé-Bcklund Transformations and Exact Solutions to a Nonlinear Diffusion Equation
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摘要 选择Painlevé-Beacklund方程组的不同解,给出一类非线性扩散方程的某些精确孤立波解.这个方法也可以用来寻找其他非线性偏微分方程的精确孤立波解. Some special types of exact solitary wave solutions for a class of nonlinear diffusion equations are obtained by choosing different types of solutions of the Painlevé-Bcklund equations.The method also can be applied to seek some special types of exact solitary wave solutions to other nonlinear PDE.
出处 《内蒙古师范大学学报(自然科学汉文版)》 CAS 2003年第2期99-103,108,共6页 Journal of Inner Mongolia Normal University(Natural Science Edition)
基金 ProjectSupportedbytheNaturalScienceFoundationofInnerMongolia(2 0 0 0 13 01) theHighEducationScienceRe searchProgramofInnerMongolia(NJ0 2 0 3 5 )
关键词 非线性扩散方程 精确孤立波解 非线性偏微分方程 Painlevé-Beacklund方程组 nonlinear diffusion equation Painlevé-Bcklund equations solitary wave solution
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  • 1Weiss J,Tabor M,Carnevale G. The Painlevé property for partial differential equations [J]. J. Math. Phys. ,1983,24:522 - 526.
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  • 3Yang Lei,Liu Jianbin,Yang Kongqing. Exact solutions of nonlinear PDE,nonllnear transformations and reduction of nonlinear PDE to a quadrature [J]. Phys. Lett. ,2001,A278:267-270.
  • 4Ames W F. Nonlinear partial differential equations in engineering [M]. New York:Academic Press,1967.
  • 5Murray J D. Mathematical biology [M]. New Yoxk:Springer,1989.

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