Heisenberg ferromagnetic spin chain with bilinear and biquadratic interactions in (2+1) dimensions

We study the nonlinear dynamics of (2 + 1) dimensional ferromagnetic (FM) spin system with bilinear and biquadratic interactions in the semiclassical limit and the dynamics is found to be governed by a new integrable fourth order nonlinear Schrodinger (NLS) equation in (2 + 1) dimensions. The integrability is identified by using Lax pair operators and soliton solutions are obtained using straightforward Darboux transformation (DT) technique. The model Hamiltonian representing (2 + 1) dimensional FM spin chain with varying bilinear and biquadratic interactions are also constructed and inhomogeneity effects are studied by performing a perturbation analysis. Moreover, the modulational instability (MI) aspects are discussed through analytical solutions and graphical illustrations. (C) 2015 Elsevier B.V. All rights reserved.