A B C
Z. Naturforsch. 67a, 141 – 146 (2012)
doi:10.5560/ZNA.2011-0070
Exact Chirped Soliton Solutions for the One-Dimensional Gross–Pitaevskii Equation with Time-Dependent Parameters
Zhenyun Qin1 and Gui Mu2
1 School of Mathematics and LMNS, Fudan University, Shanghai 200433, PR China
2 College of Mathematics and Information Science, Qujing Normal University, Qujing 655011, PR China
Received June 21, 2011 / revised October 17, 2011 / published online April 2, 2012
Reprint requests to: Z. Q.; E-mail: zyqin@fudan.edu.cn
The Gross–Pitaevskii equation (GPE) describing the dynamics of a Bose–Einstein condensate at absolute zero temperature, is a generalized form of the nonlinear Schrödinger equation. In this work, the exact bright one-soliton solution of the one-dimensional GPE with time-dependent parameters is directly obtained by using the well-known Hirota method under the same conditions as in S. Rajendran et al., Physica D 239, 366 (2010). In addition, the two-soliton solution is also constructed effectively.
Key words: Hirota Method; Gross–Pitaevskii Equation; Chirped Soliton Solution.
PACS numbers: 03.75.Lm; 05.30.Jp; 67.40.Fd
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