In this paper, the dispersion characteristics of magnetostatic surface waves (MSSW) in a nonlinear gyromagnetic medium are analytically investigated. Assuming the nonlinearity as the first order perturbation in permeability tensor of the gyromagnetic medium, the perturbation technique based on the multiple scale method is used to deduce the nonlinear dispersion relations for the MSSW. It is observed that for a given propagation constant of the MSSW the frequency decreases with microwave power. It is also observed that group velocity decreases, and as a consequence, delay time increases with power of the microwave. By evaluating the dependence of frequency on power and variation of group velocity on propagation constant within the accuracy of the perturbation theory, it is confirmed that the conditions for formation of bright soliton are not satisfied for the MSSW.

In this paper, we report the simulation studies on MSW solitons based on numerical solution of nonlinear schrodinger equation by Split Step Fourier Transform method. We have studied both magnetostatic forward volume and surface modes that satisfy opposite nonlinear conditions. The parameters used for the simulation are obtained from experiments on nonlinear characteristics of both the modes. Important soliton properties such as nonlinear power dependence, pulse shaping, formation of multisolitons are studied and compared qualitatively with the experiments.