# A new class of solutions for the multi-component extended Harry Dym equation

## TL;DR

This paper introduces a novel transformation linking two integrable systems, leading to new wave-like solutions that extend the known multi-phase solutions of the multi-component extended Harry Dym equation.

## Contribution

It presents a new point transformation between the multi-component Harry Dym and extended Harry Dym equations that generates a new class of wave-like solutions, expanding the solution space.

## Key findings

- New wave-like solutions for the multi-component extended Harry Dym equation.
- Transformation does not preserve multi-phase solution class.
- Method applicable to other integrable systems with similar properties.

## Abstract

We construct a point transformation between two integrable systems, the multi-component Harry Dym equation and the multi-component extended Harry Dym equation, that does not preserve the class of multi-phase solutions. As a consequence we obtain a new type of wave-like solutions, generalising the~multi-phase solutions of the multi-component extended Harry Dym equation. Our construction is easily transferable to other integrable systems with analogous properties.