# Benney-Lin and Kawahara equations: a detailed study through Lie symmetries and Painlev\'{e} analysis

## TL;DR

This paper investigates the integrability of Benney-Lin and Kawahara equations using Lie symmetry and Painlevé analysis, revealing integrable traveling-wave solutions and algebraic solutions for these PDEs.

## Contribution

It provides a comprehensive symmetry and singularity analysis of these equations, identifying their integrable structures and solutions.

## Key findings

- Existence of integrable traveling-wave solutions
- Application of Painlevé analysis to PDEs
- Derivation of algebraic solutions for the equations

## Abstract

We perform a detailed study on the integrability of the Benney-Lin and KdV-Kawahara equations by using the Lie symmetry analysis and the singularity analysis. We find that the equations under our consideration admit integrable travelling-wave solutions. The singularity analysis is applied for the partial differential equations and the generic algebraic solution is presented.