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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.
MSC:
35C05Solutions of PDE in closed form
35G25Initial value problems for nonlinear higher-order PDE
35C08Soliton solutions of PDE
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