scholarly journals Quasiparticles of widely tuneable inertial mass: The dispersion relation of atomic Josephson vortices and related solitary waves

2018 ◽  
Vol 4 (3) ◽  
Author(s):  
Joachim Brand ◽  
Sophie Shamailov
Keyword(s):  
Dispersion Relation ◽  
Solitary Wave ◽  
Inertial Mass ◽  
Dark Soliton ◽  
Ultracold Atom ◽  
Josephson Vortex ◽  
Low Velocity ◽  
Linear Coupling ◽  
Josephson Vortices ◽  
Vortex Solutions

Superconducting Josephson vortices have direct analogues in ultracold-atom physics as solitary-wave excitations of two-component superfluid Bose gases with linear coupling. Here we numerically extend the zero-velocity Josephson vortex solutions of the coupled Gross-Pitaevskii equations to non-zero velocities, thus obtaining the full dispersion relation. The inertial mass of the Josephson vortex obtained from the dispersion relation depends on the strength of linear coupling and has a simple pole divergence at a critical value where it changes sign while assuming large absolute values. Additional low-velocity quasiparticles with negative inertial mass emerge at finite momentum that are reminiscent of a dark soliton in one component with counter-flow in the other. In the limit of small linear coupling we compare the Josephson vortex solutions to sine-Gordon solitons and show that the correspondence between them is asymptotic, but significant differences appear at finite values of the coupling constant. Finally, for unequal and non-zero self- and cross-component nonlinearities, we find a new solitary-wave excitation branch. In its presence, both dark solitons and Josephson vortices are dynamically stable while the new excitations are unstable.

scholarly journals BRIGHT AND DARK SOLITON SOLUTIONS OF THE (2 + 1)-DIMENSIONAL EVOLUTION EQUATIONS

2014 ◽  
Vol 19 (1) ◽  
pp. 118-126 ◽  
Author(s):  
Ahmet Bekir ◽  
Adem C. Cevikel ◽  
Ozkan Guner ◽  
Sait San
Keyword(s):  
Solitary Wave ◽  
Nonlinear Equations ◽  
Evolution Equations ◽  
Boussinesq Equation ◽  
Soliton Solutions ◽  
Dark Soliton ◽  
Bright Soliton ◽  
Physical Parameters ◽  
Kp Equation ◽  
Constant Coefficients

In this paper, we obtained the 1-soliton solutions of the (2+1)-dimensional Boussinesq equation and the Camassa–Holm–KP equation. By using a solitary wave ansatz in the form of sechp function, we obtain exact bright soliton solutions and another wave ansatz in the form of tanhp function we obtain exact dark soliton solutions for these equations. The physical parameters in the soliton solutions are obtained nonlinear equations with constant coefficients.

scholarly journals Bound states of atomic Josephson vortices

2017 ◽  
Vol 95 (4) ◽  
pp. 336-339 ◽  
Author(s):  
Muhammad Irfan Qadir ◽  
Usama Tahir
Keyword(s):  
Bound States ◽  
Coupling Parameter ◽  
Bound State ◽  
Dark Soliton ◽  
Critical Value ◽  
One Dimensional ◽  
Josephson Vortices ◽  
Existence And Stability ◽  
The Stability ◽  
Bose Einstein

We study the existence and stability of the bound state Josephson vortices solution in two parallel quasi one-dimensional coupled Bose–Einstein condensates. The system can be elucidated by linearly coupled Gross–Pitaevskii equations. The purpose of this study is to investigate the effects of altering the strength of coupling between the two condensates over the stability of the bound-state Josephson vortices. It is found that the stability of bound-state Josephson vortices depends on the value of coupling strength. However, at a critical value of coupling parameter, the Josephson vortices solution transforms into a coupled dark soliton.

scholarly journals Symmetric bound states of Josephson vortices in BEC

2018 ◽  
Vol 96 (2) ◽  
pp. 208-212 ◽  
Author(s):  
Muhammad Irfan Qadir ◽  
Tehseen Zoma
Keyword(s):  
Bound States ◽  
Coupling Parameter ◽  
Bound State ◽  
Dark Soliton ◽  
Critical Value ◽  
One Dimensional ◽  
Josephson Vortices ◽  
Domain Of Existence ◽  
Existence And Stability ◽  
Bose Einstein

A system of two parallel coupled cigar-shaped Bose–Einstein condensates is considered in an effectively one-dimensional limit. The dynamics of the system is characterized by a pair of coupled nonlinear Gross–Pitaevskii equations. In particular, the existence and stability of symmetric bound states of Josephson vortices are investigated. It is realized that the symmetric bound state Josephson vortices solution persists stably in its whole domain of existence for the coupling strength. Nevertheless, the bound states solution converts into a dark soliton at a critical value of coupling parameter.

Anomalous Josephson vortex solutions in Josephson junctions with multiple tunneling channels

2010 ◽  
Vol 470 (20) ◽  
pp. 1137-1140 ◽  
Author(s):  
Y. Ota ◽  
M. Machida ◽  
T. Koyama ◽  
H. Matsumoto
Keyword(s):  
Josephson Junctions ◽  
Josephson Vortex ◽  
Vortex Solutions

scholarly journals Three-layer Non-hydrostatic Staggered Scheme for Free Surface Flow

2018 ◽  
Author(s):  
Ade Candra Bayu ◽  
Sri Redjeki Pudjaprasetya ◽  
Ikha Magdalena
Keyword(s):  
Dispersion Relation ◽  
Solitary Wave ◽  
Hydrodynamic Pressure ◽  
Flow Region ◽  
Free Surface Flow ◽  
Surface Flow ◽  
Type Model ◽  
Test Case ◽  
Staggered Scheme ◽  
Successive Over Relaxation

In this paper, a finite difference algorithm using a three-layer approximationfor the vertical flow region to solve the 2D Euler equations was considered. Inthis algorithm, the pressure was split into hydrostatic and hydrodynamic parts, and thepredictor-corrector procedure was applied. In the predictor step, the momentum hydrostaticmodel was formulated. In the corrector step, the hydrodynamic pressure wasaccommodated after solving the Laplace equation using the Successive Over Relaxation(SOR) iteration method. The resulting algorithm was first tested to simulate a standingwave over an intermediate constant depth. Dispersion relation of the scheme wasderived and it was shown to agree with the analytical dispersion relation for kd < piwith 94% accuracy. The second test case was a solitary wave simulation. Our computedsolitary wave propagated with constant velocity, undisturbed in shape, and confirmedthe analytical solitary wave. Finally, the scheme was tested to simulate the appearanceof the undular bore. The result shows a good agreement with the result from the finitevolume scheme for the Boussinesq-type model by Soares-Frazão and Guinot (2008).

scholarly journals Effect of Streaming and Finite Geometry on a Resonance-like Phenomenon in Beam-Plasma Systems

1993 ◽  
Vol 46 (6) ◽  
pp. 807
Author(s):  
J Mukhopadhyay ◽  
K Roy Chowdhury ◽  
A Roy Chowdhury
Keyword(s):  
Dispersion Relation ◽  
Solitary Wave ◽  
Finite Geometry ◽  
Plasma System ◽  
Linear Dispersion ◽  
Ion Density ◽  
Linear Dispersion Relation ◽  
Beam Plasma ◽  
Streaming Velocity ◽  
Bounded System

We have analysed the effect of finite geometry and streaming on a resonance-like phenomenon in a beam-plasma system placed in an infinite magentic field. The resonance-like phenomenon is displayed through a variation of the amplitude of the soliton with respect to a (the ratio of electron to ion density). It is shown that this event is very prominent in the case of an infinite plasma, but for a bounded system the effect is not so significant. As such, an effect of this type will be difficult to observe experimentally unless the dimension of the containment system is considerable. Furthermore, the peak of the resonance varies considerably with the streaming velocity and other parameters of the plasma. The whole phenomenon is crucially dependent on the phase velocity of the solitary wave, whose variation is also considered in detail. Lastly, it is demonstrated that the existence of a resonance-like phenomenon can also be ascertained from an analysis of the linear dispersion relation.

scholarly journals Three-Layer Non-hydrostatic Staggered Scheme for Free Surface Flow

2017 ◽  
Vol 7 (4) ◽  
pp. 643-657
Author(s):  
Ade C. Bayu ◽  
S. R. Pudjaprasetya ◽  
I. Magdalena
Keyword(s):  
Dispersion Relation ◽  
Solitary Wave ◽  
Hydrodynamic Pressure ◽  
Flow Region ◽  
Free Surface Flow ◽  
Surface Flow ◽  
Type Model ◽  
Finite Volume Scheme ◽  
Test Case ◽  
Successive Over Relaxation

AbstractIn this paper, a finite difference algorithm using a three-layer approximation for the vertical flow region to solve the 2D Euler equations is considered. In this algorithm, the pressure is split into hydrostatic and hydrodynamic parts, and the predictor-corrector procedure is applied. In the predictor step, the momentum hydrostatic model is formulated. In the corrector step, the hydrodynamic pressure is accommodated after solving the Laplace equation using the Successive Over Relaxation (SOR) iteration method. The resulting algorithm is first tested to simulate a standing wave over an intermediate constant depth. Dispersion relation of the scheme is derived, and it is shown to agree with the analytical dispersion relation for kd < π with 94% accuracy. The second test case is a solitary wave simulation. Our computed solitary wave propagates with constant velocity, undisturbed in shape, and confirm the analytical solitary wave. Finally, the scheme is tested to simulate the appearance of the undular bore. The result shows a good agreement with the result from the finite volume scheme for the Boussinesq-type model by Soares-Frazão and Guinot (2008).

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