N-Dark-Dark Solitons in the Generally Coupled Nonlinear Schroedinger Equations

TL;DR

This paper derives N-dark-dark solitons in coupled nonlinear Schrödinger equations using the KP-hierarchy reduction, revealing unique collision behaviors and bound states in defocusing and mixed nonlinear systems.

Contribution

It introduces a novel derivation of N-dark-dark solitons in coupled NLS equations and analyzes their collision and bound state properties.

Findings

Solitons exist in defocusing and mixed nonlinear regimes.

Collisions result in complete energy transmission without polarization rotation.

Two dark-dark solitons can form stationary bound states.

Abstract

N-dark-dark solitons in the generally coupled integrable NLS equations are derived by the KP-hierarchy reduction method. These solitons exist when nonlinearities are all defocusing, or both focusing and defocusing nonlinearities are mixed. When these solitons collide with each other, energies in both components of the solitons completely transmit through. This behavior contrasts collisions of bright-bright solitons in similar systems, where polarization rotation and soliton reflection can take place. It is also shown that in the mixed-nonlinearity case, two dark-dark solitons can form a stationary bound state.