Persistent bright solitons in sign-indefinite coupled nonlinear Schrödinger equations with a time-dependent harmonic trap

Abstract

We introduce a model based on a system of coupled nonlinear Schrödinger (NLS) equations with opposite signs in front of the kinetic and gradient terms in the two equations. It also includes time-dependent nonlinearity coefficients and a parabolic expulsive potential. By means of a gauge transformation, we demonstrate that, with a special choice of the time dependence of the trap, the system gives rise to persistent solitons. Exact single-and two-soliton analytical solutions and their stability are corroborated by numerical simulations. In particular, the exact solutions exhibit inelastic collisions between solitons.

Stabilization of solitons in coupled nonlinear pendulums with simultaneous external and parametric excitations

“…Equation (19) is the continuous nonlinear damped Schrodinger equation (NLS) with external and parametric excitations. When F e = 0, we obtain a parametrically driven damped nonlinear Schrdinger equation, which can be used to study intrinsic localized modes in arrays of coupled pendulums [14,22] or arrays of coupled microelectromechanical systems [7] and to model parametrically driven media in hydrodynamics [23] and optics [24,25].…”

Bright soliton dynamics in spin orbit-Rabi coupled Bose-Einstein condensates

“…It may be noted that a similar Riccati equation ( 9) has been employed to solve GP-type equations [34][35][36][37][38]. In fact, the identification of the Riccati-type equation (9) gives the first signature of complete integrability of Equation ( 1)…”

Vector Solitons of a Coupled Schrödinger System with Variable Coefficients

“…Recently, Muñoz Grajales and Quiceno [37] also illustrated the effect of these extra nonlinear terms and the parameter on modulation instability of a pulse along an optical fiber modelled by full system (1) but with constant coefficients. On the other hand, in [40], some analytical vector bright solitons were calculated for a generalized CNLS system to model BECS including self-phase modulation, cross-phase modulation coefficients, a time-dependent anti-trapping parabolic potential, and fourwave mixing nonlinear terms in the forms V 2 * and 2 V * with a time-dependent coefficient.…”