Direct perturbation theory for dark-bright solitons: Application to Bose-Einstein condensates

Abstract

We develop a direct perturbation theory for dark-bright solitons and derive evolution equations for the soliton parameters. In particular, first the linearization equation around the solitons is solved by expanding its solution into a set of complete eigenfunctions of the linearization operator. Then, suppression of secular growth in the linearized solution leads to the evolution equations of soliton parameters. The results are applied to a number of case examples motivated by the physics of atomic Bose-Einstein condensates, where dark-bright solitons have recently been studied both in theory and in experiments. We thus consider perturbations corresponding to (a) finite temperature-induced thermal losses, and (b) the presence of localized (δ-function) impurities. In these cases, relevant equations of motion for the dark-bright soliton center are in agreement with ones previously obtained via alternative methods, including energy-based methods, as well as numerical linear stability analysis and direct simulations.

Δυναμική σολιτονικών λύσεων μη-γραμμικών εξισώσεων τύπου Schrodinger

“…With the exception of the Introduction and the historical background of Chapter 1, and the review in Chapter 2, it is believed that all the work described in this thesis is original. Chapter 3, is based on paper [10], written jointly with V. M. Rothos, P. G. Kevrekidis and D. J. Frantzeskakis, published in Journal of Physics A: Mathematical and General. The results of Chapter 4, have been written up in the joint paper [11], with T. Rossides and V. M. Rothos, which has been published in The European Physical Journal Special Topics, in addition some of the results of these Chapter are part of a paper in progress.…”