Generalized spin model with vector potential and its solution

Abstract

In this work an integrable generalization of the Landau-Lifshitz equation with self - consistent vector potential is studied. It was established that self - consistence of spin vector and potential happen by the relation between solutions of the potential and linear system, the compatibility condition of which corresponds to the equation considered by us. By generalizing Hirota’s method, it’s exact solutions, defining self - consistent motion of the potential and soliton, are constructed.