Multiperiodic solutions of systems of equations with one quasi-linear differential operator in partial derivatives of the first order

Abstract

The questions of the existence and uniqueness of solution of initial and multiperiodic problem for systems of equations with quasilinear differential operator, which the vector fields are linear with respect to the given functions, is being investigated. The system, in particular, in the onedimensional case becomes as Hopf equation, which describes the propagation of waves along the axis. In this work we establish sufficient conditions for the existence and uniqueness of solution of the initial problem for the system and multiperiodic solution of system for the time variables.