Toda-Heisenberg chain: interacting sigma-fields in two dimensions

Abstract: We study a (2+1)-dimensional system that can be viewed as an infinite number of O(3) sigma-fields coupled by a nearest-neighbour Heisenberg-like interaction. We reduce the field equations of this model to an integrable system that is closely related to the two-dimensional relativistic Toda chain and the Ablowitz-Ladik equations. Using this reduction we obtain the dark-soliton solutions of our model.