We present the modification of the inverse scattering problem to integrate the sine-Gordon equation and to study the solitons and waves for magnets with a spiral (stripe domain) structure. We use the technique of "dressing" the partial solution of sine-Gordon equation by means of Riemann problem on a torus, which is related with periodic spiral structure.

The "dressing" technique allows us to study the soliton and multi-soliton solutions against the spiral structure background in detail. We also discuss the ways of observing and exciting the solitons in the spiral structure of magnets.