容许多项式子空间的四阶非线性平方算子的分类

摘要

利用不变子空间方法研究四阶非线性平方算子，确定出四阶非线性平方算子在其所容许的多项式不变子空间中的完全分类，进一步求出相应方程的爆破解。所得结果推广了不变子空间理论在非线性偏微分方程中的应用。%By using invariant subspace method ,the fourth‐order nonlinear quadratic operators is 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 e‐quations with fourth‐order nonlinear quadratic operators are constructed .The obtaining results further extend the applications of invariant subspace theory in the PDEs .