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 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.

5 pages, 6 figures, (Physical Review E, in press)

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Cited by in corpus (13)

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• Modulation of localized solutions in quadratic-cubic nonlinear Schrödinger equation with inhomogeneous coefficients
• Boundary scattering in the ${\varphi }^6$ model
• Gaussian-like and flat-top solitons of atoms with spatially modulated repulsive interactions
• Effective equations for repulsive quasi-1D BECs trapped with anharmonic transverse potentials
• Asymmetric localized states in periodic potentials with a domain wall-like Kerr nonlinearity
• Accurate one-dimensional effective description of realistic matter-wave gap solitons
• Making the PT symmetry unbreakable
• Correlations and synchronization in a Bose-Fermi mixture
• Analyzing lump-type solutions in scalar field models through configurational information measure
• Saturable nonlinear Schrödinger equation with space- and time-dependent variable coefficients