Wave-breaking and generic singularities of nonlinear hyperbolic equations

TL;DR

This paper analytically and numerically investigates wave-breaking phenomena in nonlinear hyperbolic equations, demonstrating that power laws and singular behaviors predicted by theory align well with simulations, highlighting the effectiveness of nonlinear science methods.

Contribution

It provides a detailed analytical framework for wave-breaking in nonlinear hyperbolic equations and validates it through numerical simulations, emphasizing the role of generic nonlinear science concepts.

Findings

Power laws accurately describe singularity onset.

Analytical results match numerical simulations.

Wave-breaking behavior is governed by universal singularities.

Abstract

Wave-breaking is studied analytically first and the results are compared with accurate numerical simulations of 3D wave-breaking. We focus on the time dependence of various quantities becoming singular at the onset of breaking. The power laws derived from general arguments and the singular behavior of solutions of nonlinear hyperbolic differential equations are in excellent agreement with the numerical results. This shows the power of the analysis by methods using generic concepts of nonlinear science.