期刊
SCIENCE CHINA-MATHEMATICS
卷 55, 期 9, 页码 1769-1778出版社
SCIENCE PRESS
DOI: 10.1007/s11425-012-4408-9
关键词
invariant subspace; generalized separation of variables; evolution equation
资金
- State Administration of Foreign Experts Affairs of China
- National Natural Science Foundation of China [10971136, 10831003, 61072147, 11071159]
- Chunhui Plan of the Ministry of Education of China
- Zhejiang Innovation Project [T200905]
- Natural Science Foundation of Shanghai
- Shanghai Leading Academic Discipline Project [J50101]
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 on the resulting theory, and two concrete examples are given to find invariant subspaces associated with 2nd-order and 3rd-order linear ordinary differential equations and their corresponding exact solutions with generalized separated variables.
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