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Invariant subspaces and exact solutions of a class of dispersive evolution equations. (English) Zbl 1250.35057
Summary: The invariant subspace method is used to classify a class of systems of nonlinear dispersive evolution equations and determine their invariant subspaces and exact solutions. A crucial step is to take subspaces of solutions to linear ordinary differential equations as invariant subspaces that systems of evolution equations admit. A few examples of presenting exact solutions with generalized separated variables illustrate the effectiveness of the invariant subspace method in solving systems of nonlinear evolution equations.

35C05Solutions of PDE in closed form
35G25Initial value problems for nonlinear higher-order PDE
35C08Soliton solutions of PDE
Full Text: DOI
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