Application of Karpman-Maslov-Solov’ev soliton perturbation theory to systems with distributed gain or losses

Abstract

We analyze the most important ideas of the Karpman-Maslov-Solov’ev soliton perturbation theory, and based on it, we solve analytically the long-standing problem of the Schrödinger soliton interactions in the systems with distributed losses or gain. Our analytical results do give a quite good qualitative and quantitative check of the numerical results known so far. Unexpected and nontrivial result consists in the fact that the relative soliton separation depends on the accumulated (integrated) losses or gain.