Kaptsov, O. V. Invariants of characteristics of some systems of partial differential equations. (Russian, English) Zbl 1052.35053 Sib. Mat. Zh. 45, No. 3, 577-591 (2004); translation in Sib. Math. J. 45, No. 3, 475-487 (2004). The author introduces the notion of an invariant of characteristics for a system of first-order partial differential equations. He proves that the existence of invariants is connected with passiveness of some systems. The author describes a few methods for the construction of new invariants from those already known and gives a scheme for application of the invariants to reduction and integration of systems of partial differential equations. As an application he considers the equation of gas dynamics. Reviewer: V. Grebenev (Novosibirsk) MSC: 35F20 Nonlinear first-order PDEs 35A30 Geometric theory, characteristics, transformations in context of PDEs 35Q58 Other completely integrable PDE (MSC2000) 58J70 Invariance and symmetry properties for PDEs on manifolds 76N15 Gas dynamics (general theory) Keywords:Darboux’s method; invariant set; equation of gas dynamics PDFBibTeX XMLCite \textit{O. V. Kaptsov}, Sib. Mat. Zh. 45, No. 3, 577--591 (2004; Zbl 1052.35053); translation in Sib. Math. J. 45, No. 3, 475--487 (2004) Full Text: EuDML EMIS