Bright and dark soliton solutions in growing Bose-Einstein condensates - 宋伟为 李秋艳 李再东 傅广生 (Chinese physics B, 2010)
This paper develops the Hirota method carefully for applying into the growing model of quasi-one-dimensional Bose Einstein condensations with attractive and repulsive interaction, respectively. After a tedious calculation it obtains the exact bright and dark soliton solutions analytically. It shows that the growing model has the important effect on the soliton amplitude and the time-dependent potential only contributes to the phase and phase velocity. A detailed analysis for the asymptotic behaviour of two-soliton solutions shows that the collision of two soliton is elastic.