scholarly journals Orbital stability of traveling waves for the one-dimensional Gross–Pitaevskii equation

2009 ◽  
Vol 91 (2) ◽  
pp. 178-210 ◽  
Author(s):  
Patrick Gérard ◽  
Zhifei Zhang
Keyword(s):  
Traveling Waves ◽  
Orbital Stability ◽  
Pitaevskii Equation ◽  
One Dimensional ◽  
The One

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

scholarly journals Traveling Waves for Delayed Cellular Neural Networks with Nonmonotonic Output Functions

2014 ◽  
Vol 2014 ◽  
pp. 1-11 ◽  
Author(s):  
Zhi-Xian Yu ◽  
Rong Yuan ◽  
Cheng-Hsiung Hsu ◽  
Ming-Shu Peng
Keyword(s):  
Neural Networks ◽  
Traveling Waves ◽  
Signal Transmission ◽  
Distributed Delay ◽  
Traveling Wave Solutions ◽  
Cellular Neural Networks ◽  
Switching Speed ◽  
One Dimensional ◽  
The One ◽  
Nondecreasing Functions

This work investigates traveling waves for a class of delayed cellular neural networks with nonmonotonic output functions on the one-dimensional integer latticeZ. The dynamics of each given cell depends on itself and its nearestmleft orlright neighborhood cells with distributed delay due to, for example, finite switching speed and finite velocity of signal transmission. Our technique is to construct two appropriate nondecreasing functions to squeeze the nonmonotonic output functions. Then we construct a suitable wave profiles set and derive the existence of traveling wave solutions by using Schauder's fixed point theorem.

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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