Theoretical investigation of solitons in bose einstein condensates

Abstract

The present thesis is devoted to the identification of bright solitons newlinein BoseEinstein Condensates by analytically and numerically solving the newlineGrossPitaevskii equation which give rise to bright dark and grey solitons newlineThese three types of solitons are localized excitations normally associated newlinewith integrable dynamical systems exhibiting fascinating collisional newlinedynamics Study of these collisional dynamics besides their transmission and newlineinteraction can be suitably exploited to get a better understanding of the newlinedynamical system under consideration Thus the aim of undertaking the newlinepresent thesis is three fold namely newlineTo apply an analytical technique to solve the nonlinear partial newlinedifferential equation namely the GrossPitaevskii equation newlineand to gain an understanding of the BoseEinstein newlineCondensate Among several analytical tools for solving newlinenonlinear problems in BoseEinstein Condensates like newlineinverse scattering transform Painleve analysis and gauge newlinetransformation we chose the Darboux transformation newlinetechnique Darboux transformation along with the Lax newlinetechnique is a natural choice due to its systematic and simple newlinealgebraic algorithm compared to the other methods available newlinein research literature newlineTo investigate the numerical tools for solving the same newlinenonlinear problems We took up three different numerical newlinemethods namely the SplitStep Fourier Method Crank newlineNicolson Finite Difference Method and the SplitStep Crank newlineNicolson Method already available in the literature in order to newlinecompare the merits and demerits of each technique newlineFinally to provide data to the experimentalists on the ideal newlineconditions for creation of various types of solitons we newlineperformed realistic numerical simulations on our theoretical newlinemodel of the BoseEinstein condensate newlineThis thesis is organized into six chapters The first chapter newlineprovides a general overview of the BoseEinstein Condensates and the Gross newlinePitaevskii equation which is the theoretical model to study the properties of a newlineBEC in the mean field regime newline newline