Study On Non-linear Transmission In BEC

The essence of the Einstein Bose Einstein condensate is a quantum statistical phenomenon,which is a gaseous macro quantum effect of the boson below the critical temperature state.This cohesion is the cohesion in the momentum space,which is the quantum space of the momentum space from disorder to order.In the Bose Einstein condensate state,a large number of different energy atoms suddenly are condensed into the same energy state,usually the lowest energy quantum state,which makes things that is difficult to observe the single atom quantum behavior becomes easy to study,and presents a series of very interesting physical properties.After achieving Bose-Einstein condensate in alkali metal gas,and many different physical phenomena have been studied in the wave of Einstein condensates,such as solitons,vortex,symmetry breaking,chaos for the study of Bose-Einstein condensate,mostly based on the average field approximation theory,it provides a direction for theoretical research.Based on the mean field theory,the nonlinear Schrodinger equation is obtained in the one-dimensional Bose Einstein condensates.of the analysis of the soliton behavior of Bose Einstein condensate.The main contents are as follows:Firstly,a quasi-one-dimensional Bose-Einstein condensate model is established based on the econometric analysis of bosons,based on the average field approximation method of Bose-Einstein condensate theory.The G-P equation of Bose-Einstein condensate in one-dimensional case is studied,and its analytic solution for dark soliton solution and bright soliton in the absence of external situation are studied.Secondly,The numerical solution of the nonlinear Schrodinger equation is studied by using the C-N algorithm,the BESP mechanism,the BEFD mechanism,the TSSP mechanism and the solitons under different coupling intensities under the resonant potential by Matlab based on the BEFD mechanism.Width and amplitude varies in the coupling intensities between atoms.Based on the TSSP mechanism,the collision behavior of two-component BEC soliton is simulated.Finally,Darboux transform method based on AKNS system is used to solve the quasi one-dimensional Bose-Einstein condensation model with linear potential and harmonic potential,and the corresponding analytic bright soliton solution and dark soliton solution are obtained.The width,amplitude,velocity and acceleration of the soliton solution of the soliton under the wave of Einstein condensate are studied,and the information contained in these functions is given.Hope we can bring some value to the control of the soliton.