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

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.