Soliton excitations and stability in a square lattice model of ferromagnetic spin system

We investigate the nature of nonlinear spin excitations in a square lattice model of ferromagnetic (FM) spin system with bilinear and biquadratic interactions. Using the coherent state ansatz combined with the Holstein-Primakoff (HP) bosonic representation of spin operators, the dynamics is found to be governed by a discrete nonlinear equation which possesses soliton solution. The modulational instability aspects of the soliton excitations are analysed for small perturbations in wave vectors.