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arXiv · 1012.5470

Hirota method for the nonlinear Schr\H{o}dinger equation with an arbitrary linear time-dependent potential

Zai-Dong Li·Qiu-Yan Li·Xing-Hua Hu·Zhong-Xi Zheng·Yu-Bao Sun
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Abstract

In this paper, a Hirota method is developed for applying to the nonlinear Schr\"odinger equation with arbitrary time-dependent linear potential which denotes the dynamics of soliton solutions in quasi-one-dimensional Bose-Einstein condensation. The nonlinear Schr\"odinger equation is decoupled to two equations carefully. With a reasonable assumption the one- and two-soliton solutions are constructed analytically in the presence of an arbitrary time-dependent linear potential.

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Zai-Dong Li, Qiu-Yan Li, Xing-Hua Hu, Zhong-Xi Zheng, Yu-Bao Sun. 2010-12-25. Hirota method for the nonlinear Schr\H{o}dinger equation with an arbitrary linear time-dependent potential. https://doi.org/10.1016/j.aop.2006.11.012

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