Author： Kaptsov O.V.
Publisher： Springer Publishing Company
ISSN： 0037-4466
Source： Siberian Mathematical Journal, Vol.43, Iss.3, 2002-05, pp. : 428-438
Disclaimer: Any content in publications that violate the sovereignty, the constitution or regulations of the PRC is not accepted or approved by CNPIEC.
Abstract
We introduce the notion of an invariant solution relative to an involutive distribution. We give sufficient conditions for existence of such a solution to a system of differential equations. In the case of an evolution system of partial differential equations we describe how to construct auxiliary equations for functions determining differential constraints compatible with the original system. Using this theorem, we introduce linear and quasilinear defining equations which enable us to find some classes of involutive distributions, nonclassical symmetries, and differential constraints. We present examples of reductions and exact solutions to some partial differential equations stemming from applications.
Related content
Invariant equations defining coincident root loci
Archiv der Mathematik, Vol. 83, Iss. 5, 2004-11 ,pp. :
Access to resources
Recommend
On a universal perturbative invariant of 3-manifolds
By Le T.T.Q. Murakami J. Ohtsuki T.
Topology, Vol. 37, Iss. 3, 1998-05 ,pp. :