Wave solutions for hyperbolic systems

TL;DR

This paper introduces a reduction method to find generalized traveling wave solutions for first-order quasilinear hyperbolic systems, with applications to fluid dynamics involving source terms.

Contribution

It presents a novel reduction procedure for hyperbolic systems to identify traveling wave solutions satisfying additional differential constraints.

Findings

Successfully applied to a barotropic fluid model with source term

Provides a systematic way to derive wave solutions for complex hyperbolic systems

Enhances understanding of wave behavior in nonhomogeneous hyperbolic PDEs

Abstract

In this paper we propose a reduction procedure for determining generalized travelling waves for first order quasilinear hyperbolic nonhomogeneous systems. The basic idea is to look for solutions of the governing model which satisfy a further set of differential constraints. Some applications are given for a barotropic fluid with a source term.