# On Whitham and related equations

## TL;DR

This paper investigates the dynamics of Whitham and related equations through theoretical and numerical methods, establishing bounds with KdV solutions and exploring behaviors beyond traditional water wave modeling regimes.

## Contribution

It provides rigorous bounds between Whitham and KdV solutions and offers new insights into the equation's dynamics outside standard water wave regimes.

## Key findings

- Established bounds between Whitham and KdV solutions
- Numerical simulations reveal dynamics outside typical water wave regimes
- Insights into the validity range of the Whitham equation

## Abstract

The aim of this paper is to study, via theoretical analysis and numerical simulations, the dynamics of Whitham and related equations. In particular we establish rigorous bounds between solutions of the Whitham and KdV equations and provide some insights into the dynamics of the Whitham equation in different regimes, some of them being outside the range of validity of the Whitham equation as a water waves model.