Conditional Lie-Backlund symmetries to inhomogeneous nonlinear diffusion equations

被引：0

作者：

Di, Yanmei ^{[1
]}

Zhang, Danda ^{[1
]}

Shen, Shoufeng ^{[1
]}

Zhang, Jun ^{[1
]}

机构：

[1] Zhejiang Univ Technol, Dept Appl Math, Hangzhou 310023, Zhejiang, Peoples R China

来源：

APPLIED MATHEMATICAL MODELLING | 2014年 / 38卷 / 17-18期

基金：

中国国家自然科学基金;

关键词：

Conditional Lie-Backlund symmetry; Invariant subspace; Nonlinear diffusion equation; Finite-dimensional dynamical system; BOUSSINESQ EQUATION; DIFFERENTIAL-EQUATIONS; SIMILARITY REDUCTIONS; POTENTIAL SYMMETRIES; GROUP CLASSIFICATION; CONVECTION; ABSORPTION;

D O I：

10.1016/j.apm.2014.02.020

中图分类号：

T [工业技术];

学科分类号：

08 ;

摘要：

In this paper, conditional Lie-Backlund symmetry method is used to classify a class of inhomogeneous nonlinear diffusion equations u(t) = e(-qx)(e(px)w(u)u(x))(x). Equations admitted conditional Lie-Backlund symmetries can be either solved exactly or reduced to finite-dimensional dynamical systems. A number of concrete examples defined on the exponential and trigonometric invariant subspaces are considered to illustrate this method. (C) 2014 Elsevier Inc. All rights reserved.

引用

页码：4409 / 4416

页数：8

共 37 条

[1] [Anonymous], PHYS D
[2] [Anonymous], 2004, Geometric Sturmian Theory of Nonlinear Parabolic Equations and Applications
[3] Bluman G. W., 2013, Symmetries and Differential Equations, V81
[4] BLUMAN GW, 1969, J MATH MECH, V18, P1025
[5] Nonclassical symmetry reductions of the Boussinesq equation
Clarkson, PA
[J]. CHAOS SOLITONS & FRACTALS, 1995, 5 (12) : 2261 - 2301
[6] NEW SIMILARITY REDUCTIONS OF THE BOUSSINESQ EQUATION
CLARKSON, PA
KRUSKAL, MD
[J]. JOURNAL OF MATHEMATICAL PHYSICS, 1989, 30 (10) : 2201 - 2213
[7] GENERALIZED CONDITIONAL SYMMETRIES AND EXACT-SOLUTIONS OF NONINTEGRABLE EQUATIONS
FOKAS, AS
LIU, QM
[J]. THEORETICAL AND MATHEMATICAL PHYSICS, 1994, 99 (02) : 571 - 582
[8] NONLINEAR-INTERACTION OF TRAVELING WAVES OF NONINTEGRABLE EQUATIONS
FOKAS, AS
LIU, QM
[J]. PHYSICAL REVIEW LETTERS, 1994, 72 (21) : 3293 - 3296
[9] FUSCHYCH WI, 1994, J NONLINEAR MATH PHY, V1, P60
[10] Galaktionov VA., 2007, Exact solutions and invariant subspaces of nonlinear partial differential equations in mechanics and physics

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