Nonlinear excitations in a Hamiltonian spin-field model in 2+1 dimensions

A spin-field model in two space and one time dimensions is proposed and investigated using a bilinearization technique. This model, which can be considered as a modified version of the Ishimori system, allows a Hamiltonian formulation, a symmetry algebra of Kac-Moody type with a loop-algebra structure, and the conformal invariance property. Many nonlinear excitations are found, which turn out to be of the helical and roton type, meronlike configurations endowed with a fractional topological charge, radially symmetric solutions, and domain walls. Our results are compared with those of the study of the O(3) nonlinear σ model and the Ishimori system. Finally, the physical role of both our model and the Ishimori system is discussed in the light of certain reduced equations which find applications in the theory of vortex filaments in liquid ⁴He and in dealing with the two spin-correlation functions of the two-dimensional Ising model in the scaling limit.