2014/07/31 by E. G. Charalampidis, P. G. Kevrekidis, D. J. Frantzeskakis +2
Mathematics · Physics and Astronomy · #Classical mechanics #Cold Atom Physics and Bose-Einstein Condensates #Dispersion (optics) #Mathematical analysis #Mathematical physics #Mathematics #Nonlinear Photonic Systems #Nonlinear Schrödinger equation #Nonlinear Waves and Solitons #Nonlinear system #Physics #Quantum electrodynamics #Quantum mechanics #Schrödinger's cat #nlin.PS
paper · pdf · doi:10.1103/physreve.91.012924
published as Phys. Rev. E 91, 012924 (2015) · 16 pages, 10 Figures
openalex publication_date 2015/01/26 · arxiv created 2015/01/27 · arxiv updated 2015/01/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/06
We study a two-component nonlinear Schrödinger system with equal, repulsive cubic interactions and different dispersion coefficients in the two components. We consider states that have a dark solitary wave in one component. Treating it as a frozen one, we explore the possibility of the formation of bright-solitonic structures in the other component. We identify bifurcation points at which such states emerge in the bright component in the linear limit and explore their continuation into the nonlinear regime. An additional analytically tractable limit is found to be that of vanishing dispersion of the bright component. We numerically identify regimes of potential stability, not only of the single-peak ground state (the dark-bright soliton), but also of excited states with one or more zero crossings in the bright component. When the states are identified as unstable, direct numerical simulations are used to investigate the outcome of the instability development. Although our principal focus is on the homogeneous setting, we also briefly touch upon the counterintuitive impact of the potential presence of a parabolic trap on the states of interest.