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A refined invariant subspace method and applications to evolution equations

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Abstract

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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Authors and Affiliations

  1. Department of Mathematics and Statistics, University of South Florida, Tampa, FL, 33620-5700, USA

    Wen-Xiu Ma

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  1. Wen-Xiu Ma
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Ma, WX. A refined invariant subspace method and applications to evolution equations. Sci. China Math. 55, 1769–1778 (2012). https://doi.org/10.1007/s11425-012-4408-9

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  • DOI: https://doi.org/10.1007/s11425-012-4408-9

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