Stable dipole solitons and soliton complexes in the nonlinear Schrodinger equation with periodically modulated nonlinearity

TL;DR

This paper classifies and analyzes various soliton solutions in a nonlinear Schrödinger equation with a periodically modulated nonlinearity, revealing new dipole solitons and their stability properties relevant to Bose-Einstein condensates and nonlinear optics.

Contribution

It introduces a new classification of solitons in a nonlinear lattice with sign-changing nonlinearity and identifies a previously unconsidered branch of stable dipole solitons.

Findings

Existence of two branches of dipole solitons with one being stable.

Stable dipole solitons can transform into fundamental solitons.

Numerical and analytical methods confirm the stability and properties of these solitons.

Abstract

We develop a general classification of the infinite number of families of solitons and soliton complexes in the one-dimensional Gross-Pitaevskii/nonlinear Schrodinger equation with a nonlinear lattice pseudopotential, i.e., periodically modulated coefficient in front of the cubic term, which takes both positive and negative local values. This model finds direct implementations in atomic Bose-Einstein condensates and nonlinear optics. The most essential finding is the existence of two branches of dipole solitons (DSs), which feature an antisymmetric shape, essentially squeezed into a single cell of the nonlinear lattice. This soliton species was not previously considered in nonlinear lattices. We demonstrate that one branch of the DS family (namely, the one which obeys the Vakhitov-Kolokolov criterion) is stable, while unstable DSs spontaneously transform into stable fundamental solitons (FSs). The results are obtained in numerical and approximate analytical forms, the latter based on the variational approximation. Some stable bound states of FSs are found too.