On globally smooth oscillating solutions of non-strictly hyperbolic systems

TL;DR

This paper identifies a class of non-strictly hyperbolic quasilinear systems with globally smooth oscillatory solutions near equilibrium, where oscillation periods are independent of initial conditions, and discusses their physical relevance.

Contribution

It introduces a new class of hyperbolic systems with unique oscillatory properties and explores their potential physical applications in plasma physics.

Findings

Existence of globally smooth oscillating solutions near zero stationary state

Oscillation period independence from initial conditions

Application to cold plasma equations

Abstract

A class of non-strictly hyperbolic systems of quasilinear equations with oscillatory solutions of the Cauchy problem, globally smooth in time in some open neighborhood of the zero stationary state, is found. For such systems, the period of oscillation of solutions does not depend on the initial point of the Lagrangian trajectory. The question of the possibility of constructing these systems in a physical context is also discussed, and non-relativistic and relativistic equations of cold plasma are studied from this point of view.