Planar and linear solitons in superfluid<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mmultiscripts><mml:mrow><mml:mi mathvariant="normal">He</mml:mi></mml:mrow><mml:mprescripts/><mml:mrow/><mml:mrow><mml:mn>3</mml:mn></mml:mrow><mml:mrow/><mml:mrow/></mml:mmultiscripts></mml:mrow></mml:math>

Abstract

A means of classifying the planar and linear topological textures in superfluid phases of $^{3}\mathrm{He}$ by taking into account the effects of both magnetic field and boundary conditions is described. The method of the conventional homotopic groups is applied. The structure and stability of various solitons is considered in detail. This method may be applied to the description of topologically stable solitons in other ordered systems.