Next Article in Journal
Image Intelligent Detection Based on the Gabor Wavelet and the Neural Network
Next Article in Special Issue
Nonclassical Symmetries of a Nonlinear Diffusion–Convection/Wave Equation and Equivalents Systems
Previous Article in Journal
The Design and Analysis of a Secure Personal Healthcare System Based on Certificates
Previous Article in Special Issue
Lorentz Transformations from Intrinsic Symmetries
Open AccessArticle

Invariant Subspaces of the Two-Dimensional Nonlinear Evolution Equations

1
College of Mathematics and Computer Science, Anhui Normal University, Wuhu 241000, Anhui, China
2
Center for Nonlinear Studies, Ningbo University, Ningbo 315211, Zhejiang, China
*
Author to whom correspondence should be addressed.
Academic Editor: Roman M. Cherniha
Symmetry 2016, 8(11), 128; https://doi.org/10.3390/sym8110128
Received: 1 September 2016 / Revised: 3 November 2016 / Accepted: 7 November 2016 / Published: 15 November 2016
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. View Full-Text
Keywords: symmetry group; invariant subspace; conditional Lie–Bäcklund symmetry; finite-dimensional dynamical system; nonlinear differential operator symmetry group; invariant subspace; conditional Lie–Bäcklund symmetry; finite-dimensional dynamical system; nonlinear differential operator
MDPI and ACS Style

Zhu, C.; Qu, C. Invariant Subspaces of the Two-Dimensional Nonlinear Evolution Equations. Symmetry 2016, 8, 128. https://doi.org/10.3390/sym8110128

AMA Style

Zhu C, Qu C. Invariant Subspaces of the Two-Dimensional Nonlinear Evolution Equations. Symmetry. 2016; 8(11):128. https://doi.org/10.3390/sym8110128

Chicago/Turabian Style

Zhu, Chunrong; Qu, Changzheng. 2016. "Invariant Subspaces of the Two-Dimensional Nonlinear Evolution Equations" Symmetry 8, no. 11: 128. https://doi.org/10.3390/sym8110128

Find Other Styles
Note that from the first issue of 2016, MDPI journals use article numbers instead of page numbers. See further details here.

Article Access Map by Country/Region

1
Search more from Scilit
 
Search
Back to TopTop