Classical and Quantum Mechanical (QM) Effects in the One-Soliton solution of the EM Nonlinear Schrodinger (NLS) Equation

TL;DR

This paper investigates classical and quantum effects in the one-soliton solution of the electromagnetic nonlinear Schrödinger equation, focusing on dispersion, Kerr interactions, and integrability.

Contribution

It introduces a coupled Hamiltonian-Momentum operator framework to analyze quantum effects in soliton propagation within dispersive waveguides.

Findings

Classical one-soliton solutions are derived.

Quantum effects are incorporated into the soliton analysis.

The integrability condition is applied to the NLS equation.

Abstract

Propagation effects are analyzed for electromagnetic (EM) waves which satisfy the one-soliton non-linear Schrodinger (NLS) equation in a dispersive wave guide. The coupling between momentum and frequencies due to dispersion relation is treated by a coupled Hamiltonian-Momentum operator with equal-space commutation relations(CR). Kerr interactions in the soliton are treated. The classical solution of the one-soliton with possible quantum effects are analyzed. The integrability of nonlinear equations is related to compatibility-condition for scattering matrices and such relation is applied to the NLS equation.