An algorithmic method for showing existence of nontrivial non-classical symmetries of partial differential equations without solving determining equations

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:411

Article

Chaolu, Temuer¹  Bluman, G.² 

[1] Shanghai Maritime Univ, Dept Math, Shanghai 201306, Peoples R China

[2] Univ British Columbia, Dept Math, Vancouver, BC V6T 1Z2, Canada

关键词: Non-classical symmetry;    Partial differential equations;    Differential characteristic set;    Existence;    Algorithm;   

DOI  :  10.1016/j.jmaa.2013.09.040

来源: Elsevier

【 摘 要 】

In this paper, based on differential characteristic set theory and the associated algorithm (also called Wu's method), an algorithmic method is presented to decide on the existence of a nontrivial non-classical symmetry of a given partial differential equation without solving the corresponding nonlinear determining system. The theory and algorithm give a partial answer for the open problem posed by P.A. Clarkson and E.L. Mansfield in [21] on non-classical symmetries of partial differential equations. As applications of our algorithm, non-classical symmetries and corresponding invariant solutions are found for several evolution equations. (C) 2013 Elsevier Inc. All rights reserved.

【 授权许可】

Free