Complex Toda lattice and its application to the theory of interacting optical solitons

Abstract

A class of linear and nonlinear dynamical problems that arise when studying the modulation of trains of nearly identical soliton pulses of the nonlinear Schrödinger equation is introduced. In the simplest case the dynamics of the nonlinear Schrödinger equation can be reduced to an equation that is a complex extension of the integrable Toda lattice equation, so that the latter asymptotically models the former in the case of large intersoliton separations.