# KdV-like solitary waves in two-dimensional FPU-lattices

## TL;DR

This paper proves the existence of solitary waves in two-dimensional FPU lattices in the KdV limit, extending previous results to include arbitrary directions and non-unidirectional profiles through asymptotic analysis.

## Contribution

It generalizes prior work by allowing for arbitrary propagation directions and complex wave profiles in 2D FPU lattices.

## Key findings

- Existence of solitary waves in 2D FPU lattices established.
- Generalization to arbitrary directions and non-unidirectional profiles.
- Use of asymptotic analysis of integral equations.

## Abstract

We prove the existence of solitary waves in the KdV limit of two-dimensional FPU-type lattices using asymptotic analysis of nonlinear and singularly perturbed integral equations. In particular, we generalize the existing results by Friesecke and Matthies since we allow for arbitrary propagation directions and non-unidirectional wave profiles.