Dynamics of $\vartheta$-solitons in the HPD state of superfluid ${}^3$He-B

In this note we present numerical study of spin dynamics of $\vartheta$-soliton in Homogeneously precessing domain (HPD) in superfluid ${}^3$He-B. The soliton consists of a small heavy core and long tails, in 1D simulation we observe their mutual motion. We also discuss mass density and tension of the soliton membrane and its 3D oscillations in a cylindrical cell.