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Classification and Reduction of Generalized Thin Film Equations

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Communications in Theoretical Physics 2009年第9期52卷 403-410页

作者： zhu chun-rong qu chang-zheng center for nonlinear studies Northwest University Xi＇an 710069 China College of Mathematics and Computer Science Anhui Normal University Wuhu 241000 China Department of Mathematics Northwest University Xi＇an 710069 China

Classification and reduction of the generalized fourth-order nonlinear differential equations arising from theliquid films are *** is shown that these equations have solutions on subspaces of the polynomial,exponential ortrigonometric form defined by linear nth-order ordinary differential equations with constant coefficients for n=4,...,*** examples of exact solutions are presented.

关键词： thin film equation classification invariant subspaces exact solutions

Potential Symmetries to a System of Three-Component nonlinear Diffusion Equations

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Communications in Theoretical Physics 2006年第2期45卷 193-198页

作者： XUE chun-rong qu chang-zheng center for nonlinear studies Northwest University Xi＇an 710069 China Department of Mathematics Northwest University Xi＇an 710069 China

A system of nonlinear diffusion equations with three components is studied via the potential symmetry method. It is shown that the system admits the potential symmetries for certain diffusion terms. The invariant solu... 详细信息

关键词： Lie point symmetry potential symmetry nonlinear diffusion equation group-invariant solutions

Invariant Sets and Exact Solutions to Higher-Dimensional Wave Equations

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Communications in Theoretical Physics 2008年第5期49卷 1119-1124页

作者： qu Gai-zhu ZHANG Shun-Li zhu chun-rong center for nonlinear studies Department of Mathematics Northwest University Xi＇an 710069 China center of nonlinear Science Ningbo University Ningbo 315211 China Department of Mathematics Anhui Normal University Wuhu 241000 China

The invariant sets and exact solutions of the （1 ＋ 2）-dimensional wave equations are discussed. It is shown that there exist a class of solutions to the equations which belong to the invariant set E0 = {u ： ux = ... 详细信息

关键词： wave equation invariant set exact solution

Functional Separable Solutions of nonlinear Heat Equations in Non-Newtonian Fluids

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Communications in Theoretical Physics 2008年第2期49卷 257-262页

作者： GOU Ming qu chang-zheng center for nonlinear studies Northwest University Xi＇an 710069 China Department of Mathematics Northwest University Xi＇an 710069 China

We study the functional separation of variables to the nonlinear heat equation： ut = （A（x）D（u）ux^n）x＋ B（x）Q（u）, Ax≠0. Such equation arises from non-Newtonian fluids. Its functional separation of variables is studied by using the group foliation method. A classification of the equation which admits the functional separable solutions is performed. As a consequence, some solutions to the resulting equations are obtained.

关键词： group foliation method functional separation of variable nonlinear heat equation symmetry group

Nonlocal Symmetries to Systems of nonlinear Diffusion Equations

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Communications in Theoretical Physics 2008年第1期49卷 9-16页

作者： qu chang-zheng KANG Jing center for nonlinear studies Northwest University Xi＇an 710069 China Department of Mathematics Northwest University Xi＇an 710069 China

In this paper, we study potential symmetries to certain systems of nonlinear diffusion equations. Thosesystems have physical applications in soil science, mathematical biology, and invariant curve flows in R^3. Lie point symmetries of the potential system, which cannot be projected to vector fields of the given dependent and independent variables, yield potential symmetries. The class of the system that admits potential symmetries is expanded.

关键词： symmetry group system of nonlinear diffusion equation nonlocal symmetry

Solutions and Conditional Lie-Backlund Symmetries of quasi-linear Diffusion-Reaction Equations

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Communications in Theoretical Physics 2009年第1期51卷 6-12页

作者： ZUO Su-Li qu chang-zheng center for nonlinear studies Northwest University Xi＇an 710069 China Department of Mathematics Northwest University Xi＇an 710069 China

New classes of exact solutions of the quasi-linear diffusion-reaction equations are obtained by seeking for the high-order conditional Lie-Baeklund symmetries of the considered equations. The method used here extends the approaches of derivative-dependent functional separation of variables and the invariant subspace. Behavior to some solutions such as blow-up and quenching is also described.

关键词： conditional Lie-Backlund symmetry exact solution quasi-linear diffusion-reaction equation

Extended Group Foliation Method and Functional Separation of Variables to nonlinear Wave Equations

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Communications in Theoretical Physics 2005年第4X期44卷 577-582页

作者： qu chang-zheng ZHANG Shun-Li center for nonlinear studies Northwest University Xi'an 710069 China Department of Mathematics Northwest University Xi'an 710069 China

Generalized functional separation of variables to nonlinear evolution equations is studied in terms of the extended group foliation method, which is based on the Lie point symmetry method. The approach is applied to nonlinear wave equations with variable speed and external force. A complete classification for the wave equation which admits functional separable solutions is presented. Some known results can be recovered by this approach.

关键词： symmetry group group foliation method nonlinear wave equation functional separation of variables

Higher-Dimensional Integrable Systems Arising from Motions of Curves on S^2(R)and S^3(R)

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Communications in Theoretical Physics 2008年第10期50卷 841-843页

作者： qu chang-zheng LI Yan-Yan center for nonlinear studies Northwest University Xi＇an 710069 China Department of Mathematics Northwest University Xi＇an 710069 China

We show that higher-dimensional integrable systems including the (2+1)-dimensional generalized sine-Gordon equation and the (2+1)-dimensional complex mKdV equation are associated with motions of surfaces inducedby end... 详细信息

关键词： higher-dimensional integrable system motion of curve sine-Gordon equation complex mKdV equation

Functional Separable Solutions to nonlinear Diffusion Equations by Group Foliation Method

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Communications in Theoretical Physics 2007年第2期47卷 193-199页

作者： HU Jia-Yi qu chang-zheng YIN Hui center for nonlinear studies Northwest University Xi＇an 710069 China Department of Mathematics Northwest University Xi＇an 710069 China Department of Mathematics South-Central University of Nationalities Wuhan 430074 China Wuhan Institute of Physics and Mathematics the Chinese Academy of Sciences Wuhan 430071 China

We consider the functional separation of variables to the nonlinear diffusion equation with source and convection term： ut = （A（x）D（u）ux）x ＋ B（x）Q（u）, Ax ≠ 0. The functional separation of variables to this equation is studied by using the group foliation method. A classification is carried out for the equations which admit the function separable solutions. As a consequence, some solutions to the resulting equations are obtained.

关键词： group foliation method functional separation of variable nonlinear diffusion equation symmetry group