Lump Solutions of the Ishimori-II Equation : Condensed Matter and Statistical Physics

It is known that the Ishimori-II equation has the lump solutions decaying polynomially in all directions, which are called the multi-vortex (and multi-antivortex) solutions, they are constructed by Hirota's method and ∂^-dressing method. In this paper we construct rational solutions of the Ishimori-II equation by means of the Darboux transformation and show that they contain not only the multi-vortex solutions obtained by Hirota's method as a special case, but also new lump solutions,such as mixed vortex-antivortex solutions and a one-vortex solution which circulates with a constant angular velocity.