Bright solitons from the nonpolynomial Schrödinger equation with inhomogeneous defocusing nonlinearities

W. B. Cardoso, J. Zeng, A. T. Avelar, D. Bazeia, B. A. Malomed

Research output: Contribution to journalArticlepeer-review

Abstract

Extending the recent work on models with spatially nonuniform nonlinearities, we study bright solitons generated by the nonpolynomial self-defocusing (SDF) nonlinearity in the framework of the one-dimensional (1D) Muñoz-Mateo-Delgado (MM-D) equation (the 1D reduction of the Gross-Pitaevskii equation with the SDF nonlinearity), with the local strength of the nonlinearity growing at |x|→∞ faster than |x|. We produce numerical solutions and analytical ones, obtained by means of the Thomas-Fermi approximation, for nodeless ground states and for excited modes with one, two, three and four nodes, in two versions of the model, with steep (exponential) and mild (algebraic) nonlinear-modulation profiles. In both cases, the ground states and the single-node ones are completely stable, while the stability of the higher-order modes depends on their norm (in the case of the algebraic modulation, they are fully unstable). Unstable states spontaneously evolve into their stable lower-order counterparts.

Original languageEnglish
Article number025201
JournalPhysical Review E - Statistical, Nonlinear, and Soft Matter Physics
Volume88
Issue number2
DOIs
StatePublished - 30 Aug 2013

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