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arXiv · 1306.6213

Bright solitons from the nonpolynomial Schrödinger equation with inhomogeneous defocusing nonlinearities

W. B. Cardoso·J. Zeng·A. T. Avelar·D. Bazeia·B. A. Malomed
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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 any rate faster than |x| at large values of coordinate x. We produce numerical solutions and analytical ones, obtained by means of the Thomas-Fermi approximation (TFA), for nodeless ground states, and for excited modes with 1, 2, 3, and 4 nodes, in two versions of the model, with the 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.

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W. B. Cardoso, J. Zeng, A. T. Avelar, D. Bazeia, B. A. Malomed. 2013-08-10. Bright solitons from the nonpolynomial Schrödinger equation with inhomogeneous defocusing nonlinearities. https://doi.org/10.1103/physreve.88.025201

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