Families of fundamental and multipole solitons in a cubic-quintic nonlinear lattice in fractional dimension

TL;DR

This paper explores families of fundamental and multipole solitons in a fractional Schrödinger equation with cubic-quintic nonlinearities modulated by a nonlinear lattice, analyzing their shapes, stability, and dependence on the Levy index.

Contribution

It introduces the construction and stability analysis of multipole solitons in a fractional nonlinear lattice with cubic-quintic terms, highlighting the influence of the Levy index.

Findings

Fundamental solitons are similar to those in uniform nonlinearity models.

Multipole complexes exist only with the nonlinear lattice.

Stability regions vary with the Levy index and soliton type.

Abstract

We construct families of fundamental, dipole, and tripole solitons in the fractional Schr\"{o}dinger equation (FSE)\ incorporating self-focusing cubic and defocusing quintic terms modulated by factors $\cos ^{2}x$ and $\sin^{2}x$, respectively. While the fundamental solitons are similar to those in the model with the uniform nonlinearity, the multipole complexes exist only in the presence of the nonlinear lattice. The shapes and stability of all the solitons strongly depend on the L\'{e}vy index (LI)\ that determines the FSE fractionality. Stability areas are identified in the plane of LI and propagation constant by means of numerical methods, and some results are explained with the help of an analytical approximation. The stability areas are broadest for the fundamental solitons and narrowest for the tripoles.