A refined invariant subspace method and applications to evolution equations

The invariant subspace method is refined to present more unity and more diversity of exact solutions to evolution equations. The key idea is to take subspaces of solutions to linear ordinary differential equations as invariant subspaces that evolution equations admit. A two-component nonlinear syste...

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Bibliographic Details
Published inScience China. Mathematics Vol. 55; no. 9; pp. 1769 - 1778
Main Author Ma, Wen-Xiu
Format Journal Article
LanguageEnglish
Published Heidelberg SP Science China Press 01.09.2012
Subjects
Applications of Mathematics
Differential equations
Evolution
Exact solutions
Invariants
Mathematical analysis
Mathematical models
Mathematics
Mathematics and Statistics
Subspace methods
Subspaces
不变子空间
子空间方法
应用
演化方程
空间变量
线性常微分方程
非线性发展方程
非线性系统
37K35
37J15
generalized separation of variables
evolution equation
35A24
invariant subspace
37K40
Online AccessGet full text
ISSN1674-7283
1869-1862
DOI10.1007/s11425-012-4408-9

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Summary:The invariant subspace method is refined to present more unity and more diversity of exact solutions to evolution equations. The key idea is to take subspaces of solutions to linear ordinary differential equations as invariant subspaces that evolution equations admit. A two-component nonlinear system of dissipative equations is analyzed to shed light oi1 the resulting theory, and two concrete examples are given to find invariant subspaces associated with 2nd-order and 3rd-order linear ordinary differentii equations and their corresponding exact solutions with generalized separated variables.
Bibliography:invariant subspace, generalized separation of variables, evolution equation
The invariant subspace method is refined to present more unity and more diversity of exact solutions to evolution equations. The key idea is to take subspaces of solutions to linear ordinary differential equations as invariant subspaces that evolution equations admit. A two-component nonlinear system of dissipative equations is analyzed to shed light oi1 the resulting theory, and two concrete examples are given to find invariant subspaces associated with 2nd-order and 3rd-order linear ordinary differentii equations and their corresponding exact solutions with generalized separated variables.
11-1787/N
MA Wen-Xiu Department of Mathematics and Statistics, University of South Florida, Tampa, FL 33620-5700, USA Email： mawx@cas.usf.edu
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ISSN:1674-7283
1869-1862
DOI:10.1007/s11425-012-4408-9