Stabilization of solitons under competing nonlinearities by external potentials

Journal Article · Mon Dec 15 04:00:00 EST 2014 · Chaos (Woodbury, N. Y.)

DOI:https://doi.org/10.1063/1.4903359· OSTI ID:22402517

Karpierz, Miroslaw A. ^[1]; Wasak, Tomasz; Trippenbach, Marek ^[2]; Malomed, Boris A. ^[3]

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1. Faculty of Physics, Warsaw University of Technology, Warsaw, ul. Koszykowa 75, PL-00-662 Warszawa (Poland)
2. Faculty of Physics, University of Warsaw, ul. Hoza 69, PL-00-681 Warszawa (Poland)
3. Department of Physical Electronics, School of Electrical Engineering, Faculty of Engineering, Tel Aviv University, Tel Aviv 69978 (Israel)

We report results of the analysis for families of one-dimensional (1D) trapped solitons, created by competing self-focusing (SF) quintic and self-defocusing (SDF) cubic nonlinear terms. Two trapping potentials are considered, the harmonic-oscillator (HO) and delta-functional ones. The models apply to optical solitons in colloidal waveguides and other photonic media, and to matter-wave solitons in Bose-Einstein condensates loaded into a quasi-1D trap. For the HO potential, the results are obtained in an approximate form, using the variational and Thomas-Fermi approximations, and in a full numerical form, including the ground state and the first antisymmetric excited one. For the delta-functional attractive potential, the results are produced in a fully analytical form, and verified by means of numerical methods. Both exponentially localized solitons and weakly localized trapped modes are found for the delta-functional potential. The most essential conclusions concern the applicability of competing Vakhitov-Kolokolov (VK) and anti-VK criteria to the identification of the stability of solitons created under the action of the competing SF and SDF terms.

• OSTI ID: 22402517
• Journal Information: Chaos (Woodbury, N. Y.), Journal Name: Chaos (Woodbury, N. Y.) Journal Issue: 4 Vol. 24; ISSN CHAOEH; ISSN 1054-1500
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
BOSE-EINSTEIN CONDENSATION
ELECTRIC POTENTIAL
GROUND STATES
HARMONIC OSCILLATORS
NONLINEAR PROBLEMS
ONE-DIMENSIONAL CALCULATIONS
SOLITONS
STABILITY
THOMAS-FERMI MODEL
TRAPPING
VARIATIONAL METHODS