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

Journal Article · Fri Jul 15 04:00:00 EDT 2016 · Chaos (Woodbury, N. Y.)

DOI:https://doi.org/10.1063/1.4958710· OSTI ID:22596609

We develop a general classification of the infinite number of families of solitons and soliton complexes in the one-dimensional Gross-Pitaevskii/nonlinear Schrödinger 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.

• OSTI ID: 22596609
• Journal Information: Chaos (Woodbury, N. Y.), Journal Name: Chaos (Woodbury, N. Y.) Journal Issue: 7 Vol. 26; ISSN CHAOEH; ISSN 1054-1500
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
97 MATHEMATICS AND COMPUTING
BOSE-EINSTEIN CONDENSATION
DIPOLES
NONLINEAR OPTICS
NONLINEAR PROBLEMS
ONE-DIMENSIONAL CALCULATIONS
PERIODICITY
SCHROEDINGER EQUATION