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

• The dynamics of (2 + 1) dimensional ferromagnetic (FM) spin system is described.
• The solitonic aspects related to both homogeneous and inhomogeneous systems are studied.
• Multi-soliton solutions to the resulting completely integrable (2 + 1)dimensional fourth order NLS equation are constructed.
• The stability of solitons in the inhomogeneous level is studied.

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.