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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-{2. qu chang-zheng center for nonlinear {2. 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 {2. chang-zheng center for nonlinear {2. 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

Stimulated Brillouin interaction between guided phonons and photons in a lithium niobate waveguide

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Science china(Physics,Mechanics & Astronomy) 2024年第1期67卷 173-175页

作者： Yuan-Hao Yang Jia-Qi Wang zheng-Xu zhu Xin-Biao Xu Qiang Zhang Juanjuan Lu Yu Zeng {2.-Hua Dong Luyan Sun Guang-Can Guo chang-Ling Zou CAS Key Laboratory of quantum Information University of Science and Technology of ChinaHefei 230026China CAS center for Excellence in quantum Information and quantum Physics University of Science and Technology of ChinaHefei 230026China Key Laboratory of quantum Optics and quantum Optics Devices Institute of Opto-ElectronicsShanxi UniversityTaiyuan 030006China School of Information Science and Technology ShanghaiTech UniversityShanghai 201210China center for quantum Information Institute for Interdisciplinary Information SciencesTsinghua UniversityBeijing 100084China

The Brillouin scattering is one of the strongest nonlinear optical effects in dielectrics[1].In particular,the backward Brillouin scattering(BBS)provides an efficient method to achieve low-noise optical gain for active photonics[2.and the coherent interconnects between 10 GHz phonons and photons[3].However,previous {2. on BBS are primarily limited to the unconfined phonons[1]or phonon confined in suspended structures[4-6].

关键词： scattering waveguide Brillouin

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 {2. 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-{2. center for nonlinear {2. 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-{2. KANG Jing center for nonlinear {2. 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-{2. center for nonlinear {2. 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-{2. ZHANG Shun-Li center for nonlinear {2. 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-{2. LI Yan-Yan center for nonlinear {2. 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