# Peakon and kink solutions for a system of $0-$Holm-Staley equations

## TL;DR

This paper investigates a two-component Holm-Staley system, deriving explicit peakon and kink solutions, and analyzing their unique behaviors compared to scalar cases, with implications for nonlinear wave dynamics.

## Contribution

It introduces explicit multipeakon and multikink solutions for a two-component Holm-Staley system, expanding understanding of their structure and symmetry properties.

## Key findings

- Explicit 1-peakon and 1-kink solutions derived
- Solutions exhibit behaviors different from scalar equations
- Conditions for multipeakon and multikink existence identified

## Abstract

In this paper we consider a two-component system of the Holm-Staley equation with no stretching and a one-parameter nonlinearity in the convection term. Point symmetries are found, conditions for the existence of multipeakon and multikink solutions are determined. Solutions for the 1-peakon and 1-kink are explicitly obtained and they exhibit a behaviour quite different of their analogous in the scalar equation.