Classical Forces on Solitons in Finite and Infinite, Nonlinear, Planar Waveguides

TL;DR

This paper derives and compares classical force densities on solitons in various nonlinear waveguides using conservation laws and quantum mechanics analogies, enhancing understanding of soliton dynamics.

Contribution

It introduces a novel approach to analyze soliton forces by combining conservation equations with quantum analogy methods in different waveguide configurations.

Findings

Conservation equations for soliton densities are established.

Classical force densities are derived and compared with quantum analogy results.

Insights into soliton behavior in finite and infinite waveguides are provided.

Abstract

Conservation equations for the mass, linear momentum and energy densities of solitons propagating in finite, infinite and periodic, nonlinear, planar waveguides and governed by the nonlinear Schr\"odinger equation are derived. These conservation equations are used to determine classical force densities which are compared with those derived by drawing a quantum mechanics analogy between the propagation of solitons and the motion of a quantum particle in a nonlinear potential well.