Stable dipole solitons and soliton complexes in the nonlinear Schr€odinger equation with periodically modulated nonlinearity

M. E. Lebedev, G. L. Alfimov, Boris A. Malomed

Research output: Contribution to journalArticlepeer-review

Abstract

We develop a general classification of the infinite number of families of solitons and soliton complexes in the one-dimensional Gross-Pitaevskii/nonlinear Schr€odinger 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, being 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, 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. Published by AIP Publishing.

Original languageEnglish
Article number073110
JournalChaos
Volume26
Issue number7
DOIs
StatePublished - 1 Jul 2016

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