Applying canonical transformations to the nonlinear Schrödinger equation for modeling fiber optic communications

Abstract

This paper presents a numerical implementation of a novel algorithm for modeling optical signal propagation under the nonlinear Schrödinger equation. Rooted in the Hamiltonian formalism and canonical transformations, the method is mathematically rigorous and devoid of empirical techniques. We investigate the algorithm’s properties and range of applicability both analytically and numerically, highlighting its advantages over existing methods. An extension is also developed to include dissipative effects. The proposed approach is applied to various wave fields, and its performance is compared with standard dispersion and nonlinear phase compensation techniques. These initial results demonstrate the potential of the algorithm for fiber-optic communication applications.