Soliton Dynamics in Linearly Coupled Discrete Nonlinear Schrödinger Equations

Abstract

We study soliton dynamics in a system of two linearly coupled discrete nonlinear Schrödinger 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.

to be published in Mathematics and Computers in Simulation, proceedings of the fifth IMACS International Conference on Nonlinear Evolution Equations and Wave Phenomena: Computation and Theory (Athens, Georgia - April 2007)