Wave breaking for the generalized Fornberg-Whitham equation

TL;DR

This paper investigates wave breaking phenomena in a generalized Fornberg-Whitham equation, demonstrating that solutions can develop singularities for large initial slopes and discussing the equation's dispersive characteristics.

Contribution

It establishes wave breaking conditions for a generalized Fornberg-Whitham equation with weak dispersion, extending understanding of singularity formation in such models.

Findings

Wave breaking occurs for large initial slopes.

Dispersive properties of the generalized equation are analyzed.

Conditions for singularity formation are identified.

Abstract

This paper aims to show that the Cauchy problem of the Burgers equation with a weakly dispersive perturbation involving the Bessel potential (generalization of the Fornberg-Whitham equation) can exhibit wave breaking for initial data with large slope. We also comment on the dispersive properties of the equation.