Bright solitons from the nonpolynomial Schrödinger equation with inhomogeneous defocusing nonlinearities
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2013
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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) Mu˜noz-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.
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W. B. Cardoso; ZENG, J.; AVELAR, A. T.; BAZEIA, D.; MALOMED, B. A. Bright solitons from the nonpolynomial Schrödinger equation with inhomogeneous defocusing nonlinearities. Physical Review. E, Melville, v. 88, e025201, 2013.