保持多项式子空间的三阶非线性平方算子的分类

Classification of Third-order Nonlinear Quadratic Operators Preserving Polynomial Subspaces

利用不变子空间方法研究三阶非线性平方算子,得到了三阶非线性平方算子在它所容许的多项式不变子空间中的分类,从而求出相应方程的精确解。文中的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。

Using the invariant subspace method,the third-order nonlinear quadratic operators is discussed,the full classifications of polynomial invariant subspace admitted by the third-order quadratic operators are derived,moreover,some explicit solutions to the resulting evolution equations with third-order nonlinear quadratic operators are constructed. The obtaining results further extend the applications of invariant subspace theory in the PDEs.