Dromion and Lump Solutions of the Ishimori-I Equation

Abstract

It is known that the Ishimori-I equation, which is the (2+1)-dimensional generalization of the classical continuous Heisenberg ferromagnet equation, has various localized solutions such as the dromion, lump and rationally-exponentially localized solutions. In this paper localized solutions of the Ishimori-I equation are constructed explicitly in terms of grammian determinants by using the binary Darboux transformation, and it is shown that they include not only the multi-soliton (dromion, lump and so on) solutions but also new localized solutions.