Modulation of localized solutions in quadratic-cubic nonlinear Schrödinger equation with inhomogeneous coefficients
arXiv:1704.03348 · doi:10.1016/j.cnsns.2017.01.012
Abstract
We study the presence of exact localized solutions in a quadratic-cubic nonlinear Schrödinger equation with inhomogeneous nonlinearities. Using a specific ansatz, we transform the nonautonomous nonlinear equation into an autonomous one, which engenders composed states corresponding to solutions localized in space, with an oscillating behavior in time. Direct numerical simulations are employed to verify the stability of the modulated solutions against small random perturbations.
12 pages, 8 figures
References in corpus (9)
- Tuning the scattering length with an optically induced Feshbach resonance
- Localized nonlinear waves in systems with time- and space-modulated nonlinearities
- Dipolar gases in quasi one-dimensional geometries
- Solitons with Cubic and Quintic Nonlinearities Modulated in Space and Time
- Effective mean-field equations for cigar-shaped and disk-shaped Bose-Einstein condensates
- Exact solutions to three-dimensional generalized nonlinear Schrodinger equations with varying potential and nonlinearities
- Effective Nonlinear Schrödinger Equations for Cigar-Shaped and Disk-Shaped Fermi Superfluids at Unitarity
- Effective one-dimensional dynamics of elongated Bose-Einstein condensates
- Unidimensional reduction of the 3D Gross-Pitaevskii equation with two- and three-body interactions