An integrable model of (2+1)-dimensional Heisenberg ferromagnetic spin chain and soliton excitations

We investigate the nonlinear spin dynamics of (2+1)-dimensional Heisenberg ferromagnetic (FM) spin chains with bilinear and anisotropic interactions in the semiclassical limit using the coherent state ansatz combined with the Holstein–Primakoff (HP) bosonic representation of spin operators. In the continuum limit the dynamics is found to be governed by a new integrable nonlinear Schrödinger type equation in (2+1) dimensions. The integrability of the equation is studied by constructing Lax pair of operators. The multisoliton solution is generated through the Darboux transformation. We also propose a model representing the (2+1)-dimensional inhomogeneous Heisenberg FM spin chain and the effect of inhomogeneity is understood by performing a perturbation analysis. Finally, the modulation instability aspects are discussed via analytic solutions and graphical illustrations.