delta -dressing and exact solutions for the (2+1)-dimensional Harry Dym equation

Abstract

Exact implicit solutions with functional parameters of the (2+1)-dimensional Harry Dym (HD) equation are constructed by the delta -dressing method. The interrelation between the HD and modified Kadomtsev-Petviashvili (mKP) equations is established within the framework of the delta -dressing method. Knowledge of the mKP eigenfunctions allows the solutions of the (2+1)-dimensional HD equation to be represented in a simple parametric form.