Dispersionless evolution of inviscid nonlinear pulses

TL;DR

This paper studies the evolution of nonlinear non-dispersive waves in one dimension, introducing an approximate scheme for the Euler-Poisson equation that is accurate across various systems and provides wave breaking time estimates.

Contribution

It proposes a novel approximate method for solving the Euler-Poisson equation in nonlinear wave dynamics, applicable to diverse systems and exact for monoatomic gases.

Findings

The scheme is exact for monoatomic classical gas.

It agrees well with exact solutions and simulations for other systems.

Provides accurate wave breaking time estimates.

Abstract

We consider the one-dimensional dynamics of nonlinear non-dispersive waves. The problem can be mapped onto a linear one by means of the hodograph transform. We propose an approximate scheme for solving the corresponding Euler-Poisson equation which is valid for any kind of nonlinearity. The approach is exact for monoatomic classical gas and agrees very well with exact results and numerical simulations for other systems. We also provide a simple and accurate determination of the wave breaking time for typical initial conditions.