Solitons in geometric potentials

TL;DR

This paper investigates how geometric potentials in undulated waveguides influence soliton behavior, revealing stability differences, new stable multipole solitons, and barriers to transverse motion, advancing understanding of soliton dynamics in structured media.

Contribution

It demonstrates the significant impact of geometric potentials on soliton stability, thresholds, and mobility, introducing new stable multipole solitons supported by undulated waveguides.

Findings

Solitons in potential maxima are stable and thresholdless.

Solitons in potential minima are unstable and may require a power threshold.

Stable multipole solitons are supported by the geometric potential.

Abstract

We show that the geometrically-induced potential existing in undulated slab waveguides dramatically affects the properties of solitons. In particular, whereas solitons residing in the potential maxima do not feature power thresholds and are stable, their counterparts residing in the potential minima are unstable and may exhibit a power threshold for their existence. Additionally, the geometric potential is shown to supports stable multipole solitons that cannot be supported by straight waveguides. Finally, the geometric potential results in the appearance of the effective barriers that prevent transverse soliton motion.