scholarly journals Stability in the energy space for chains of solitons of the one-dimensional Gross-Pitaevskii equation

2014 ◽  
Vol 64 (1) ◽  
pp. 19-70 ◽  
Author(s):  
Fabrice Béthuel ◽  
Philippe Gravejat ◽  
Didier Smets
Keyword(s):  
Energy Space ◽  
Pitaevskii Equation ◽  
One Dimensional ◽  
The One

Bright solitons in the one-dimensional discrete Gross-Pitaevskii equation with dipole-dipole interactions

2008 ◽  
Vol 78 (6) ◽  
Author(s):  
Goran Gligorić ◽  
Aleksandra Maluckov ◽  
Ljupčo Hadžievski ◽  
Boris A. Malomed
Keyword(s):  
Pitaevskii Equation ◽  
One Dimensional ◽  
Bright Solitons ◽  
Dipole Interactions ◽  
The One

Exact Chirped Soliton Solutions for the One-Dimensional Gross– Pitaevskii Equation with Time-Dependent Parameters

2012 ◽  
Vol 67 (3-4) ◽  
pp. 141-146 ◽  
Author(s):  
Zhenyun Qina ◽  
Gui Mu
Keyword(s):  
Soliton Solution ◽  
Soliton Solutions ◽  
Einstein Condensate ◽  
Time Dependent ◽  
Pitaevskii Equation ◽  
Zero Temperature ◽  
One Dimensional ◽  
Bose Einstein Condensate ◽  
The One ◽  
Bose Einstein

The Gross-Pitaevskii equation (GPE) describing the dynamics of a Bose-Einstein condensate at absolute zero temperature, is a generalized form of the nonlinear Schr¨odinger 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

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