Slow Soliton Interaction with Delta Impurities
نویسندگان
چکیده
We study the Gross-Pitaevskii equation with a delta function potential, qδ0, where |q| is small and analyze the solutions for which the initial condition is a soliton with initial velocity v0. We show that up to time (|q|+ v 0)− 1 2 log(1/|q|) the bulk of the solution is a soliton evolving according the classical dynamics of a natural effective Hamiltonian, (ξ + q sech(x))/2.
منابع مشابه
Fast Soliton Scattering by Delta Impurities
We study the Gross-Pitaevskii equation with a repulsive delta function potential. We show that a high velocity incoming soliton is split into a transmitted component and a reflected component. The transmitted mass (L norm squared) is shown to be in good agreement with the quantum transmission rate of the delta function potential. We further show that the transmitted and reflected components res...
متن کاملSoliton Splitting by External Delta Potentials
We show that a soliton scattered by an external delta potential splits into two solitons and a radiation term. Theoretical analysis gives the amplitudes and phases of the reflected and transmitted solitons with errors going to zero as the velocity of the incoming soliton tends to infinity. Numerical analysis shows that this asymptotic relation is valid for all but very slow solitons. We also sh...
متن کاملResonant and Non-resonant Soliton Scattering by Impurities
The NLSE soliton scattering by impurities is considered in the framework of the one-dimensional model. The scattering intensity is characterized by the reflection coefficient. The reflection coefficient of the soliton is calculated in the Born approximation of the perturbation theory for the following cases: (i) and isolated impurity, (ii) two point impurities, and (iii) a regular or random sys...
متن کاملSolitons, spatiotemporal chaos and synchronization in arrays of damped driven nonlinear oscillators
We explore periodic and chaotic motion in a soliton-bearing chain of nonlinear oscillators and study the effect of disorder on the spatiotemporal chaos. The chain we consider consists of torsionally coupled, damped, parametrically driven pendulums. We show that the amplitudes of the pendulums satisfy a system of equations in slow time, the “nonlinear Schrödinger (NLS) oscillators”. The evolutio...
متن کاملSolitons in Bose–Einstein condensates
The Gross–Pitaevskii equation (GPE) describing the evolution of the Bose–Einstein condensate (BEC) order parameter for weakly interacting bosons supports dark solitons for repulsive interactions and bright solitons for attractive interactions. After a brief introduction to BEC and a general review of GPE solitons, we present our results on solitons that arise in the BEC of hard-core bosons, whi...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2007