Master partial differential equations for a Type II hidden symmetry

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:343

Article

Abraham-Shrauner, Barbara¹  Govinder, Keshlan S.² 

[1] Washington Univ, Dept Elect & Syst Engn, St Louis, MO 63130 USA

[2] Univ KwaZulu Natal, Sch Math Sci, Astrophys & Cosmol Res Unit, ZA-4041 Durban, South Africa

关键词: Lie group symmetries;    partial differential equations;    ordinary differential equations;    hidden symmetries;   

DOI  :  10.1016/j.jmaa.2008.01.074

来源: Elsevier

【 摘 要 】

An approach for determining a class of master partial differential equations from which Type II hidden point symmetries are inherited is presented. As an example a model nonlinear partial differential equation (PDE) reduced to a target PDE by a Lie symmetry gains a Lie point synnnetry that is not inherited (hidden) from the original PDE. On the other hand this Type II hidden symmetry is inherited from one or more of the class of master PDEs. The class of master PDEs is determined by the hidden symmetry reverse method. The reverse method is extended to determine symmetries of the master PDEs that are not inherited. We indicate why such methods are necessary to determine the genesis of Type II symmetries of PDEs as opposed to those that arise in ordinary differential equations (ODEs). (C) 2008 Elsevier Inc. All rights reserved.

【 授权许可】

Free