Solitons and nonlinear waves in the spiral magnetic structures

•The procedure to integrate the sine-Gordon model against the background of the spiral (stripe domain) structure is presented.•We give the complete analysis of solitons (breathers, one- and two-kink excitations) on the spiral background.•The ways of exciting these solitons are proposed.•The large-time behavior of the dispersive waves in the structure is investigated.

This paper presents a procedure to integrate the sine-Gordon model against the background of the stripe domain structure. The nonlinear dynamics of solitons and dispersive waves in the helical (stripe domain) structure of a ferromagnet with the easy plane anisotropy in the magnetic field, which is perpendicular to the spiral axis, has been investigated in detail. It has been shown that the formation and motion of solitons are accompanied by the local translations of the stripe structure and by the oscillations of its domain walls, which manifest themselves as “precursors” and “tails” of the solitons. The large time behavior of the weak-nonlinear dispersive wave field generated by an initial localized perturbation of the structure has been investigated. The ways of observing and exciting the solitons in the spiral structure of magnets and multiferroics are discussed.