title: Stabilization of solitons under competing nonlinearities by external potentials.
abstract: 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.
authors.affiliation: Faculty of Physics, Warsaw University of Technology, Warsaw, ul. Koszykowa 75, PL-00-662 Warszawa, Poland.
authors.forename: Krzysztof B
authors.initials: KB
authors.lastname: Zegadlo
authors.affiliation: Faculty of Physics, University of Warsaw, ul. Hoza 69, PL-00-681 Warszawa, Poland.
authors.forename: Tomasz
authors.initials: T
authors.lastname: Wasak
authors.affiliation: Department of Physical Electronics, School of Electrical Engineering, Faculty of Engineering, Tel Aviv University, Tel Aviv 69978, Israel.
authors.forename: Boris A
authors.initials: BA
authors.lastname: Malomed
authors.affiliation: Faculty of Physics, Warsaw University of Technology, Warsaw, ul. Koszykowa 75, PL-00-662 Warszawa, Poland.
authors.forename: Miroslaw A
authors.initials: MA
authors.lastname: Karpierz
authors.affiliation: Faculty of Physics, University of Warsaw, ul. Hoza 69, PL-00-681 Warszawa, Poland.
authors.forename: Marek
authors.initials: M
authors.lastname: Trippenbach