Calculation of the formation time for microwave magnetic envelope solitons

The theoretical formation and propagation properties of microwave magnetic envelope solitons were modeled from the nonlinear Schrodinger equation without damping. Based on soliton threshold input amplitude criteria from inverse scattering theory, input amplitudes were set midpoint between the one- and two-soliton threshold values. The soliton formation time T_s was defined as the time required for the pulse amplitude to stabilize after launch. This T_s was found to be independent of the nonlinear response coefficient N and to vary as the inverse of the dispersion coefficient D. One possible way to model these T_s dependencies is through the relation T_s≈[T_d T_nl]^1/2, where T _d and T_nl are characteristic dispersion and nonlinear response times, respectively. This result suggests a simple geometric mean relation between these characteristic times