Soliton emission in an external resonant field

A calculation is made of the power of plasma wave emission by a fluxon in a long Josephson junction induced by a variable external current with a frequency close to the plasma frequency of the junction. Also determined is the power of spin wave emission by a quasi-one-dimensional domain wall in a weak plane-parallel ferromagnetic under the effect of a variable external magnetic field with a frequency close to that of parametric resonance. The resonant emission of small-amplitude breathers (dynamic solitons) is investigated, as is the emission of a small-amplitude breather in a weak ferromagnetic due to the effect of a randomly varying field. The treatment is based on the method of the inverse scattering problem for the sine-Gordon equation in which the external field has the role of a small perturbation.