Abstract
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 Schrödinger (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.
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