# Solitary wave solutions and their interactions for fully nonlinear water waves with surface tension in the generalized Serre equations

## TL;DR

This paper investigates the effects of surface tension on fully nonlinear water waves, presenting new analytical solutions and numerical analysis of solitary wave interactions across different surface tension regimes.

## Contribution

It introduces analytical peaked traveling wave solutions at critical surface tension and compares solitary wave interactions in subcritical and supercritical regimes.

## Key findings

- Differences in solitary wave interactions across surface tension regimes
- New peaked traveling wave solutions at critical surface tension
- Numerical validation using high-accuracy finite element methods

## Abstract

Some effects of surface tension on fully-nonlinear, long, surface water waves are studied by numerical means. The differences between various solitary waves and their interactions in subcritical and supercritical surface tension regimes are presented. Analytical expressions for new peaked travelling wave solutions are presented in the case of critical surface tension. The numerical experiments were performed using a high-accurate finite element method based on smooth cubic splines and the four-stage, classical, explicit Runge-Kutta method of order four.