Invariant subspaces and exact solutions of a class of dispersive evolution equations

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.

► Obtaining subspaces of exact solutions by the refined invariant subspace method.
► Taking linear ordinary differential equations as invariant subspaces admitted.
► Exploring generalized separation of variables: u(x,t)=∑i=1Nfi(x)gi(t).