Invariant Subspaces of the Two-Dimensional Nonlinear Evolution Equations

• Main Authors: Chunrong Zhu, Changzheng Qu
• Format: Article
• Language: English
• Published: MDPI AG 2016-11-01
• Series: Symmetry
• Subjects: symmetry group; invariant subspace; conditional Lie–Bäcklund symmetry; finite-dimensional dynamical system; nonlinear differential operator
• Online Access: http://www.mdpi.com/2073-8994/8/11/128

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.