Soliton Dynamics in Linearly Coupled Discrete Nonlinear Schr\"odinger Equations

TL;DR

This paper investigates soliton dynamics in linearly coupled discrete nonlinear Schrödinger equations, revealing oscillatory behavior and comparing numerical results with effective models for different coupling regimes.

Contribution

It introduces a unitary transformation approach for equal nonlinear couplings and explores soliton behavior in coupled Ablowitz-Ladik equations, expanding understanding of multi-component Bose gases.

Findings

Solitons oscillate between species when nonlinear couplings are equal

Numerical simulations match effective two-mode model predictions

Behavior in coupled Ablowitz-Ladik equations is characterized

Abstract

We study soliton dynamics in a system of two linearly coupled discrete nonlinear Schr\"odinger equations, which describe the dynamics of a two-component Bose gas, coupled by an electromagnetic field, and confined in a strong optical lattice. When the nonlinear coupling strengths are equal, we use a unitary transformation to remove the linear coupling terms, and show that the existing soliton solutions oscillate from one species to the other. When the nonlinear coupling strengths are different, the soliton dynamics is numerically investigated and the findings are compared to the results of an effective two-mode model. The case of two linearly coupled Ablowitz-Ladik equations is also investigated.