Wave breaking for perturbed Burgers equations

TL;DR

This paper provides an explicit criterion for wave breaking in a broad class of perturbed Burgers equations, including models like Fractional KdV and Whitham, with a rigorous and straightforward proof.

Contribution

It introduces a simple, explicit wave breaking criterion applicable to various Burgers-type models, expanding understanding of wave dynamics in these equations.

Findings

Established a criterion for wave breaking in perturbed Burgers equations

Applied the criterion to models like Fractional KdV and Whitham equations

Provided a rigorous and straightforward proof of the criterion

Abstract

We establish a simple and explicit criterion for wave breaking for a general class of perturbed Burgers equations that cover several Burgers-type models, including the Fractional KdV equation, the Whitham equation, and the Fornberg-Whitham equation. The proof is both rigorous and straightforward.