Generalized conditional symmetries of evolution equations

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:379

Article

Kunzinger, Michael¹  Popovych, Roman O.^1,2 

[1] Univ Vienna, Fak Math, A-1090 Vienna, Austria

[2] NAS Ukraine, Inst Math, Kiev 4, Ukraine

关键词: Generalized conditional symmetry;    Conditional Lie-Backlund symmetry;    Evolution equation;    Exact solution;    Formal compatibility;    Passive system;   

DOI  :  10.1016/j.jmaa.2011.01.027

来源: Elsevier

【 摘 要 】

We analyze the relationship of generalized conditional symmetries of evolution equations to the formal compatibility and passivity of systems of differential equations as well as to systems of vector fields in involution. Earlier results on the connection between generalized conditional invariance and generalized reduction of evolution equations are revisited. This leads to a no-go theorem on determining equations for operators of generalized conditional symmetry. It is also shown that up to certain equivalences there exists a one-to-one correspondence between generalized conditional symmetries of an evolution equation and parametric families of its solutions. (C) 2011 Elsevier Inc. All rights reserved.

【 授权许可】

Free