Generalized perturbed complex Toda chain for Manakov system and exact solutions of Bose–Einstein mixtures

2009 ◽  
Vol 80 (1) ◽  
pp. 112-119 ◽  
Author(s):  
V.S. Gerdjikov ◽  
N.A. Kostov ◽  
E.V. Doktorov ◽  
N.P. Matsuka
Keyword(s):  
Exact Solutions ◽  
Toda Chain ◽  
Bose Einstein ◽  
Complex Toda Chain

The N-Soliton Interactions, Complex Toda Chain and Stable Propagation of NLS Soliton Trains

1999 ◽  
pp. 219-226
Author(s):  
V. S. Gerdjikov ◽  
E. G. Evstatiev ◽  
D. J. Kaup ◽  
G. L. Diankov ◽  
I. M. Uzunov
Keyword(s):  
Toda Chain ◽  
Soliton Interactions ◽  
Stable Propagation ◽  
Complex Toda Chain

scholarly journals Exact Solutions of Bose-Einstein Condensate in Linear Magnetic Field and Time-Dependent Laser Field

2011 ◽  
Vol 119 (3) ◽  
pp. 294-297 ◽  
Author(s):  
W.H. Huang ◽  
J.W. Mao ◽  
W.G. Qiu
Keyword(s):  
Magnetic Field ◽  
Exact Solutions ◽  
Laser Field ◽  
Einstein Condensate ◽  
Time Dependent ◽  
Bose Einstein Condensate ◽  
Bose Einstein

scholarly journals EXACT SOLUTIONS TO THE SPIN-2 GROSS–PITAEVSKII EQUATIONS

2012 ◽  
Vol 27 (02) ◽  
pp. 1350013 ◽  
Author(s):  
ZHI-HAI ZHANG ◽  
YONG-KAI LIU ◽  
SHI-JIE YANG
Keyword(s):  
Exact Solutions ◽  
Rotational Symmetry ◽  
Time Factors ◽  
Time Dependent ◽  
Spin Space ◽  
One Dimensional ◽  
Density Distributions ◽  
Hyperfine State ◽  
The One ◽  
Bose Einstein

We present several exact solutions to the coupled nonlinear Gross–Pitaevskii equations which describe the motion of the one-dimensional spin-2 Bose–Einstein condensates. The nonlinear density–density interactions are decoupled by making use of the properties of Jacobian elliptical functions. The distinct time factors in each hyperfine state implies a "Lamor" procession in these solutions. Furthermore, exact time-evolving solutions to the time-dependent Gross–Pitaevskii equations are constructed through the spin-rotational symmetry of the Hamiltonian. The spin-polarizations and density distributions in the spin-space are analyzed.

scholarly journals Adiabatic interaction ofNultrashort solitons: Universality of the complex Toda chain model

2001 ◽  
Vol 64 (5) ◽  
Author(s):  
V. S. Gerdjikov ◽  
E. V. Doktorov ◽  
J. Yang
Keyword(s):  
Toda Chain ◽  
Chain Model ◽  
Complex Toda Chain

Exact solutions of the Gross-Pitaevskii equation for stable vortex modes in two-dimensional Bose-Einstein condensates

2010 ◽  
Vol 81 (6) ◽  
Author(s):  
Lei Wu ◽  
Lu Li ◽  
Jie-Fang Zhang ◽  
Dumitru Mihalache ◽  
Boris A. Malomed ◽  
...  
Keyword(s):  
Exact Solutions ◽  
Pitaevskii Equation ◽  
Two Dimensional ◽  
Bose Einstein ◽  
Stable Vortex

Families of Exact Solutions for Two-Component Bose-Einstein Condensates

2010 ◽  
Vol 152-153 ◽  
pp. 1309-1312
Author(s):  
Dong Bo Cao ◽  
Liu Xian Pan ◽  
Yan Bin Sun ◽  
Jia Ren Yan
Keyword(s):  
Exact Solutions ◽  
Fiber Optics ◽  
Soliton Solutions ◽  
Trigonometric Function ◽  
Transform Method ◽  
Two Component ◽  
Trigonometric Function Solutions ◽  
Bose Einstein

Two-component Bose-Einstein condensates systems are investigated in the presented work, using the trigonometric function transform method, and several families of exact solutions are obtained for coupled two-component nonlinear Gross Pitaevskii equations. The solutions obtained in this paper include four kinds of soliton solutions and five kinds of trigonometric function solutions. Finally, the corresponding exact solutions of the uncoupled NLS equations are easy derived in fiber optics.

scholarly journals Weakly Interacting Bose-Einstein Condensates under Rotation: Mean-Field versus Exact Solutions

2001 ◽  
Vol 86 (6) ◽  
pp. 945-949 ◽  
Author(s):  
A. D. Jackson ◽  
G. M. Kavoulakis ◽  
B. Mottelson ◽  
S. M. Reimann
Keyword(s):  
Exact Solutions ◽  
Mean Field ◽  
Weakly Interacting ◽  
Field Versus ◽  
Bose Einstein
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