Invariant Subspaces of the Two-Dimensional Nonlinear Evolution Equations

作者：Chunrong Zhu, Changzheng Qu · 发表于：Symmetry · 年份：2016 · DOI：10.3390/sym8110128 · 被引用次数：16 · 研究领域：Nonlinear Waves and Solitons、Nonlinear Photonic Systems、Fractional Differential Equations Solutions

In this paper, we develop the symmetry-related methods to study invariant subspaces of the two-dimensional nonlinear differential operators. The conditional Lie–Bäcklund symmetry and Lie point symmetry methods are used to construct invariant subspaces of two-dimensional differential operators. We first apply the multiple conditional Lie–Bäcklund symmetries to derive invariant subspaces of the two-dimensional operators. As an application, the invariant subspaces for a class of two-dimensional nonlinear quadratic operators are provided. Furthermore, the invariant subspace method in one-dimensional space combined with the Lie symmetry reduction method and the change of variables is used to obtain invariant subspaces of the two-dimensional nonlinear operators.