The unified approach to integrable relativistic equations: Soliton solutions over nonvanishing backgrounds. II

Abstract

In Part I of this work the N-soliton solution has been constructed for the generic system associated with the sl(2,C) case of the scheme for the unified description of integrable relativistic massive fields. Here, solutions are isolated for reductions of this system, including the (conventional) complex sine-Gordon equation, the massive Thirring model and another complexification of the sine-Gordon equation defined by the Lagrangian L= ‖∂μφ‖2/1−‖φ‖2 +‖φ‖2−J 2μ/2‖φ‖2(1−‖φ‖2) , Jμ=i(φ*∂μφ−φ∂μφ*). The latter model is shown to exhibit decays and fusion of (subluminal) solitons. The reduction to the conventional complex sine-Gordon appears to be even more interesting as it cannot be defined by simply restricting the linear problem to some real form of sl(2,C) algebra, and the relevant involution turns out to be quite nontrivial. When the background is flat, this involution degenerates and so the N-kink solution for the reduction cannot be extracted from the generic N-kink solution directly. This difficulty is bypassed by seeing the flat background case as a limit of an exponential one.