Forces on Solitons in Finite, Nonlinear, Planar Waveguides

TL;DR

This paper investigates the forces and energies acting on solitons in finite planar waveguides with various boundary conditions, revealing how boundary hardness influences these physical quantities through a quantum analogy.

Contribution

It introduces a quantum analogy approach to analyze soliton forces and energies in finite waveguides with different boundary conditions, highlighting the impact of boundary hardness.

Findings

Force and energy densities have S-shape profiles.

Boundary condition hardness increases force and energy densities.

Quantum analogy effectively describes soliton boundary interactions.

Abstract

The forces acting on and the energies of solitons governed by the nonlinear Schr\"odinger equation in finite, planar waveguides with periodic and with homogeneous Dirichlet, Neumann and Robin boundary conditions are determined by means of a quantum analogy. It is shown that these densities have S-shape profiles and increase as the hardness of the boundary conditions is increased.