# Two dimensional solitary waves in shear flows

## TL;DR

This paper investigates the existence, properties, and asymptotic behavior of solitary wave solutions in a two-dimensional shear flow model, using variational methods and interpolation theory.

## Contribution

It introduces a novel application of the mountain pass theorem to establish solitary wave solutions for the generalized Shrira equation in two dimensions.

## Key findings

- Existence of solitary wave solutions proven.
- Regularity and decay properties established.
- Asymptotic behavior characterized.

## Abstract

In this paper we study existence and asymptotic behavior of solitary-wave solutions for the generalized Shrira equation, a two-dimensional model appearing in shear flows. The method used to show the existence of such special solutions is based on the mountain pass theorem. One of the main difficulties consists in showing the compact embedding of the energy space in the Lesbesgue spaces; this is dealt with interpolation theory. Regularity and decay properties of the solitary waves are also established.