Algebraic bright and vortex solitons in defocusing media

TL;DR

This paper shows that in certain defocusing nonlinear media with spatially increasing nonlinearity, stable bright and vortex solitons with algebraic decay can exist, expanding understanding of soliton behavior in inhomogeneous environments.

Contribution

It introduces a new class of stable bright and vortex solitons supported by inhomogeneous defocusing nonlinear landscapes with algebraic tails.

Findings

Fundamental solitons are always stable.

Vortices and multipoles are stable if nonlinearity growth is sufficiently high.

Energy flow converges when the growth rate exceeds the dimension.

Abstract

We demonstrate that spatially inhomogeneous defocusing nonlinear landscapes with the nonlinearity coefficient growing toward the periphery as [1+abs(r)]**a support one- and two-dimensional fundamental and higher-order bright solitons, as well as vortex solitons, with algebraically decaying tails. The energy flow of the solitons converges as long as nonlinearity growth rate exceeds the dimensionality, i.e., a>D. Fundamental solitons are always stable, while multipoles and vortices are stable if the nonlinearity growth rate is large enough.