Thresholds of Envelope Soliton Formation in a Weakly Dissipative Medium

Thresholds of envelope soliton formation from input rectangular pulses of amplitude $b$ and duration $T$ in a nonlinear dispersive medium with weak dissipation are calculated. The calculated threshold curve $b_{\mathrm{th}}^2=f\left({1/T}^2\right)$ has $n$ minima corresponding to the formation of $1,2,\dots ,n$ envelope solitons. The positions and magnitudes of these minima are determined by the dissipation parameter in the medium. The derived threshold formula provides a quantitative description of the threshold curve measured recently for spin wave envelope solitons in yttrium-iron-garnet films.