On compatibility of overdetermined systems for double waves.

Abstract

Obtaining equations for double waves in the case of a general quasilinear system of partial differential equations poses some difficulties. They are connected with the complexity and awkwardness of the study of overdetermined systems, describing solutions of this class. However, there are general statements about double waves of autonomous quasilinear systems of equations. This article is devoted to the classification of irreducible double waves of autonomous nonhomogeneous systems.