This article is cited in 4 papers

Invariants of characteristics of some systems of partial differential equations

O. V. Kaptsov

Institute of Computational Modelling, Siberian Branch of the Russian Academy of Sciences

Abstract: We introduce the notion of an invariant of characteristics for a system of first-order partial differential equations. We prove that the existence of invariants is connected with passiveness of some systems. We describe a few methods for construction of new invariants from those already known. We give a scheme for application of the invariants to reduction and integration of systems of partial differential equations. As an application we consider the equation of gas dynamics.

Keywords: characteristic, invariant, Darboux's method.

UDC: 517.956

Received: 27.05.2003

 English version: Siberian Mathematical Journal, 2004, 45:3, 475–487

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