Dimensional Effects on Solitonic Matter and Optical Waves with Normal and Anomalous Dispersion

TL;DR

This paper explores how the dimensionality and dispersion properties affect the behavior of bright and dark solitons in matter waves and optical systems, revealing critical density thresholds for their existence.

Contribution

It demonstrates the dependence of soliton profiles on nonlinearity strength and dispersion type in higher dimensions, extending previous one-dimensional analyses.

Findings

Bright solitons with anomalous dispersion exist under certain conditions.

Dark solitons with normal dispersion disappear at a critical density.

Profiles of solitons are influenced by nonlinearity and dispersive properties.

Abstract

We investigate bright and dark solitons with anomalous or normal dispersion and under transverse harmonic confinement. In matter waves, positive atomic mass implies anomalous dispersion (kinetic spreading) while negative mass gives normal dispersion (kinetic shrinking). We find that, contrary to the strictly one-dimensional case, the axial and transverse profiles of these solitons crucially depend on the strength of the nonlinearity and on their dispersive properties. In particular, we show that, like bright solitons with anomalous dispersion, also dark solitons with normal dispersion disappear at a critical axial density. Our predictions are useful for the study of atomic matter waves in Bose-Einstein condensates and also for optical bullets in inhomogeneous Kerr media.