title: Bright solitons from the nonpolynomial Schrödinger equation with inhomogeneous defocusing nonlinearities.
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.
authors.affiliation: Instituto de Física, Universidade Federal de Goiás, 74.001-970, Goiânia, Goiás, Brazil.
authors.forename: W B
authors.initials: WB
authors.lastname: Cardoso
authors.forename: J
authors.initials: J
authors.lastname: Zeng
authors.forename: A T
authors.initials: AT
authors.lastname: Avelar
authors.forename: D
authors.initials: D
authors.lastname: Bazeia
authors.forename: B A
authors.initials: BA
authors.lastname: Malomed