Emission from, quasi-classical quantization, and stochastic decay of sine-Gordon solitons in external fields

Abstract

Different dynamical problems for solitons (kinks and breathers) of a sine-Gordon equation perturbed by small Hamiltonian terms describing constant and variable (time-periodic or randomly varying) external fields in various physical problems, e.g. external magnetic field in weak ferromagnets and bias current in long Josephson junctions, are considered. Among these problems are energy emission generated by a soliton in variable spatially homogeneous fields (both the resonant and nonresonant cases being considered) or in constant field of an attractive micro-inhomogeneity (a magnetic impurity in a ferromagnet or a micro-resistance in a Josephson junction); perturbation-induced corrections to the quasi-classical spectrum of a quantized small-amplitude breather; stochastic decay of a weakly bound breather into a kink-antikink pair under the action of variable field or in the field of a microinhomogeneity. The influence of dissipation on the considered effects is analyzed too.