Journal of Physics A Mathematical and Theoretical

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

Ioannis Mylonas, Vassilis M. Rothos, P. G. Kevrekidis, D. J. Frantzeskakis

Published Nov 25, 2015• 2 citations

Abstract

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.

DOI: 10.1088/1751-8113/49/1/015202

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