Stable two-dimensional dispersion-managed soliton

TL;DR

This paper investigates the existence and dynamics of dispersion-managed solitons in two-dimensional nonlinear Schrödinger equations, providing analytical and numerical insights, and discusses applications to Bose-Einstein condensates in optical lattices.

Contribution

It introduces averaged equations for 2D dispersion-managed solitons and analyzes their long-term behavior and stability, including applications to matter-wave solitons in BECs.

Findings

Analytical predictions match PDE and ODE simulations.

Dispersion-managed matter-wave solitons can exist in BEC systems.

The long-time evolution of solitons is successfully described by averaged equations.

Abstract

The existence of a dispersion-managed soliton in two-dimensional nonlinear Schr\"odinger equation with periodically varying dispersion has been explored. The averaged equations for the soliton width and chirp are obtained which successfully describe the long time evolution of the soliton. The slow dynamics of the soliton around the fixed points for the width and chirp are investigated and the corresponding frequencies are calculated. Analytical predictions are confirmed by direct PDE and ODE simulations. Application to a Bose-Einstein condensate in optical lattice is discussed. The existence of a dispersion-managed matter-wave soliton in such system is shown.