A class of third-order nonlinear evolution equations admitting invariant subspaces and associated reductions

被引：0
作者：
Yujian Ye
Wen-Xiu Ma
Shoufeng Shen
Danda Zhang
机构：
[1] Hangzhou Dianzi University,School of Management
[2] University of South Florida,Department of Mathematics and Statistics
[3] Zhejiang University of Technology,Department of Applied Mathematics
来源：
Journal of Nonlinear Mathematical Physics | 2014年 / 21卷
关键词：
evolution equation; invariant subspace; separation of variables; reduction; dynamical system; 35G20;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
With the aid of symbolic computation by Maple, a class of third-order nonlinear evolution equations admitting invariant subspaces generated by solutions of linear ordinary differential equations of order less than seven is analyzed. The presented equations are either solved exactly or reduced to finite-dimensional dynamical systems. A number of concrete examples admitting invariant subspaces generated by power, trigonometric and exponential functions are computed to illustrate the resulting theory.
引用
收藏
页码：132 / 148
页数：16
相关论文
共 20 条
[1]  
Fokas AS(1994)Nonlinear interaction of travelling waves of nonintegrable equations, Phys Rev. Lett 72 3293-3296
[2]  
Liu QM(2013)Construction of exact solutions for fractional order differential equations by the invariant subspace method, Comput Math. Appl 66 576-584
[3]  
Gazizov RK(2007)Structure theorems for linear and non-linear differential operators admitting invariant polynomial subspaces, Discrete Contin. Dyn Syst 18 85-106
[4]  
Kasatkin AA(1993)Exact polynomial solutions to some nonlinear diffusion equations Physica D 64 35-65
[5]  
Gómez-Ullate D(2013)Exact solutions for pattern formation in a reaction-diffusion system Int. J. Nonlinear Sci. Numer. Simul 14 307-315
[6]  
Kamran N(2012)Maximal dimension of invariant subspaces to systems of nonlinear evolution equations Chin. Annal. Math. Series B 33 161-178
[7]  
Milson R(2013)New maximal dimension of invariant subspaces to coupled systems with two-component equations Commun. Nonlinear Sci. Numer. Simulat 18 2984-2992
[8]  
King JR(2004)Ordinary differential operators possessing invariant subspaces of polynomial type Commun. Nonlinear Sci. Numer. Simulat 9 105-115
[9]  
Lin YZ(undefined)undefined undefined undefined undefined-undefined
[10]  
Liu YP(undefined)undefined undefined undefined undefined-undefined
12