Interaction of N solitons in the massive Thirring model and optical gap system: the complex Toda chain model.

Abstract

Using the Karpman-Solov'ev quasiparticle approach for soliton-soliton interaction we show that the train propagation of N well-separated solitons of the massive Thirring model is described by the complex Toda chain with N nodes. For the optical gap system a generalized (nonintegrable) complex Toda chain is derived for description of the train propagation of well-separated gap solitons. These results are in favor of the recently proposed conjecture of universality of the complex Toda chain.