Soliton Solutions to the Mel’nikov Equations

Abstract

It is shown that the Mel’nikov equations can be considered as a system of the KP equation, its Bäcklund transformation and the two-dimensional Toda equation. Soliton solutions of bright- and dark-types for the Mel’nikov equations are derived from the Wronskian solutions of the system. The relation of solutions between the Mel’nikov equations and a system comprised of the nonlinear Schrödinger equation coupled to the Boussinesq equation is also briefly mentioned.