# Evolution of wave pulses in fully nonlinear shallow-water theory

## TL;DR

This paper studies how wave pulses evolve into dispersive shock waves in fully nonlinear shallow-water equations, providing analytical formulas and confirming them with numerical solutions.

## Contribution

It introduces simple analytical formulas for the asymptotic evolution of localized pulses in fully nonlinear shallow-water theory, validated by numerical simulations.

## Key findings

- Analytical formulas accurately describe pulse evolution.
- Dispersive shock edges are characterized within Whitham theory.
- Numerical solutions confirm the analytical predictions.

## Abstract

We consider evolution of wave pulses with formation of dispersive shock waves in framework of fully nonlinear shallow-water equations. Situations of initial elevations or initial dips on the water surface are treated and motion of the dispersive shock edges is studied within the Whitham theory of modulations. Simple analytical formulas are obtained for asymptotic stage of evolution of initially localized pulses. Analytical results are confirmed by exact numerical solutions of the fully nonlinear shallow-water equations.