Quantum difference nonlinear Schr�dinger equation

Robert G. Cawley

N. N. Frolov

J. W. G. Wignall

David W. Brown, Katja Lindenberg, Bruce J. West

Hong Liu, Wei Jia-Yu, Lou Sen‐Yue +2 more

Base on spherical symmetric trap treatment, we analyze how to change a generalized Gross-Pitaevskii equation to a quintic nonlinear Schrdinger equation. Analysing the nonlinear Schrdinger equation, we find a typical bright soliton solution in Tonks-Girardeau gas region. This will help experimental observations.

Zhiqiang Huang

This paper get a general survey of advances in Wave Mechanics.The development of Wave Mechanics goes back to ancient times.The principle of least action is the source of Wave Mechanics,so it is the mother of several principles.Erwin Schrdinger was the greatest contribution scientist of Wave Mechanics,secondary was Louis de Broglie.The Schrdinger equation not only can treat the movement of microscopic particles,but also can analysed some of the macroscopic scientific problems.There's no time for Schrdinger to study the non-linear Schrdinger equation(NLS),but de Broglie devoted oneself to the study of nonlinear Wave Mechanics,and established contact with the solitary waves.At present,the most research works involve the nonlinear differential equations in mathematics,but ignore the physical meaning.In the sciences of waves,the study of electro-magnetic waves are important field,many problems demand clarification.From the Wave Mechanics point of view,we must integrate the classic electro-magnetic wave equation with the Quantum Mechanics wave eqution,the isolated discussion age of classic fields and waves was extremely early ended.