Scheme of constructing soliton-type solutions of the (2+1)-dimensional Harry Dym equation

The scheme of constructing multisoliton solutions of the Harry Dym equation in (2+1) dimensions is presented. The general formula for N-soliton solution is obtained. The case of N = 1 is considered in detail. The analysis of the family of three-parameter solutions is performed. The plots of these solutions are presented. The auto-Bäcklund transformations for the Kadomtzev-Petviashvili, modified Kadomtzev-Petviashvili and Harry Dym-(2+1) equations are shown to be reduced to the phase shift of the corresponding soliton solutions.