Hirota method for the nonlinear Schrődinger equation with an arbitrary linear time-dependent potential

Details Hirota method for the nonlinear Schrődinger equation with an arbitrary linear time-dependent potential Hirota method for the nonlinear Schrődinger equation with an arbitrary linear time-dependent potential

2010-12-25

arxiv.org/abs/1012.5470v1

Ann.Phys. (New York) 322, 2545 (2007)

Physics

Condensed Matter

Other Condensed Matter

11 pages

Scientific paper

10.1016/j.aop.2006.11.012

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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