Classification of fourth-order nonlinear quadratic operators admitting polynomial subspaces. (Chinese. English summary) Zbl 1349.35073
Summary: By using invariant subspace method, the fourth-order nonlinear quadratic operators are studied. The full classifications of polynomial invariant subspace preserved by the fourth-order quadratic operators are derived. Moreover, some explicit solutions to the resulting evolution equations with fourth-order nonlinear quadratic operators are constructed. The obtained results further extend the applications of invariant subspace theory in PDEs.