Abstract
The necessary and sufficient conditions for soliton creation in superfluid $^{3}\mathrm{He}$, by turning off an inhomogeneous magnetic field are studied theoretically. In the $A$ phase, where the basic equation is the sine-Gordon equation, the initial value problem is solved by making use of the inverse scattering approach. In order to create pairs of solitons, two conditions have to be satisfied: first, the total impulse (i.e., the spatial integral of the turned-off field) has to be larger than a discrete set of threshold values; and secondly, the maximum Zeeman field associated with the turned-off field has to be larger than the threshold value ${\ensuremath{\omega}}_{n}$, which are functions of the total impulse. In the $B$ phase, where no analytical method is available, we resort to numerical analysis. In spite of significant difference in the dynamic equation, creation of solitons in the $B$ phase can be expressed in terms of two conditions similar to ones in the $A$ phase.
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