Three‐dimensional dark spatial solitary waves

1991 ◽  
Vol 70 (10) ◽  
pp. 5694-5696 ◽  
Author(s):  
Yijiang Chen
Keyword(s):  
Solitary Waves ◽  
Three Dimensional

Stability and instability of some nonlinear dispersive solitary waves in higher dimension

1996 ◽  
Vol 126 (1) ◽  
pp. 89-112 ◽  
Author(s):  
Anne de Bouard
Keyword(s):  
Solitary Waves ◽  
Acoustic Waves ◽  
Vries Equation ◽  
Three Dimensional ◽  
Higher Dimension ◽  
Ion Acoustic Waves ◽  
Stability And Instability ◽  
Ion Acoustic ◽  
De Vries ◽  
The Stability

We study the stability of positive radially symmetric solitary waves for a three dimensional generalisation of the Korteweg de Vries equation, which describes nonlinear ion-acoustic waves in a magnetised plasma, and for a generalisation in dimension two of the Benjamin–Bona–Mahony equation.

Ion-acoustic waves in a degenerate multicomponent magnetoplasma

2012 ◽  
Vol 79 (2) ◽  
pp. 163-168 ◽  
Author(s):  
U. M. ABDELSALAM ◽  
M. M. SELIM
Keyword(s):  
Solitary Waves ◽  
Acoustic Waves ◽  
Three Dimensional ◽  
Negative Ions ◽  
Expansion Method ◽  
Reductive Perturbation Method ◽  
Negative Ion ◽  
Zk Equation ◽  
Ion Acoustic ◽  
Astrophysical Objects

AbstractThe hydrodynamic equations of positive and negative ions, degenerate electrons, and the Poisson equation are used along with the reductive perturbation method to derive the three-dimensional Zakharov–Kuznetsov (ZK) equation. The G′/G-expansion method is used to obtain a new class of solutions for the ZK equation. At certain condition, these solutions can describe the solitary waves that propagate in our plasma. The effects of negative ion concentrations, the positive/negative ion cyclotron frequency, as well as positive-to-negative ion mass ratio on solitary pulses are examined. Finally, the present study might be helpful to understand the propagation of nonlinear ion-acoustic solitary waves in a dense plasma, such as in astrophysical objects.

scholarly journals Three-dimensional Gross–Pitaevskii solitary waves in optical lattices: Stabilization using the artificial quartic kinetic energy induced by lattice shaking

2016 ◽  
Vol 380 (1-2) ◽  
pp. 177-181 ◽  
Author(s):  
M. Olshanii ◽  
S. Choi ◽  
V. Dunjko ◽  
A.E. Feiguin ◽  
H. Perrin ◽  
...  
Keyword(s):  
Kinetic Energy ◽  
Solitary Waves ◽  
Optical Lattices ◽  
Three Dimensional

scholarly journals Dynamics of gravity–capillary solitary waves in deep water

2012 ◽  
Vol 708 ◽  
pp. 480-501 ◽  
Author(s):  
Zhan Wang ◽  
Paul A. Milewski
Keyword(s):  
Solitary Waves ◽  
Water Waves ◽  
Periodic Structures ◽  
Time Integration ◽  
Three Dimensional ◽  
Three Dimensions ◽  
Full Potential ◽  
Numerical Time Integration ◽  
The Stability ◽  
Nonlinear Focusing

AbstractThe dynamics of solitary gravity–capillary water waves propagating on the surface of a three-dimensional fluid domain is studied numerically. In order to accurately compute complex time-dependent solutions, we simplify the full potential flow problem by using surface variables and taking a particular cubic truncation possessing a Hamiltonian with desirable properties. This approximation agrees remarkably well with the full equations for the bifurcation curves, wave profiles and the dynamics of solitary waves for a two-dimensional fluid domain, and with higher-order truncations in three dimensions. Fully localized solitary waves are then computed in the three-dimensional problem and the stability and interaction of both line and localized solitary waves are investigated via numerical time integration of the equations. There are many solitary wave branches, indexed by their finite energy as their amplitude tends to zero. The dynamics of the solitary waves is complex, involving nonlinear focusing of wavepackets, quasi-elastic collisions, and the generation of propagating, spatially localized, time-periodic structures akin to breathers.

Stability analysis and applications of traveling wave solutions of three-dimensional nonlinear modified Zakharov–Kuznetsov equation in a magnetized plasma

2018 ◽  
Vol 33 (25) ◽  
pp. 1850145 ◽  
Author(s):  
Abdullah ◽  
Aly R. Seadawy ◽  
Jun Wang
Keyword(s):  
Solitary Wave ◽  
Solitary Waves ◽  
Electrostatic Field ◽  
Three Dimensional ◽  
Field Potential ◽  
Traveling Wave Solutions ◽  
Mapping Method ◽  
Magnetized Plasma ◽  
Solitary Wave Solutions ◽  
Wave Solutions

Propagation of three-dimensional nonlinear solitary waves in a magnetized electron–positron plasma is analyzed. Modified extended mapping method is further modified and applied to three-dimensional nonlinear modified Zakharov–Kuznetsov equation to find traveling solitary wave solutions. As a result, electrostatic field potential, electric field, magnetic field and quantum statistical pressure are obtained with the aid of Mathematica. The new exact solitary wave solutions are obtained in different forms such as periodic, kink and anti-kink, dark soliton, bright soliton, bright and dark solitary waves, etc. The results are expressed in the forms of trigonometric, hyperbolic, rational and exponential functions. The electrostatic field potential and electric and magnetic fields are shown graphically. The soliton stability of these solitary wave solutions is analyzed. These results demonstrate the efficiency and precision of the method that can be applied to many other mathematical physical problems.

scholarly journals Large three-dimensional ellipsoid sphere-shaped structure of electrostatic solitary waves in the terrestrial bow shock under condition of Ωce/ωpe < < 1

2013 ◽  
Vol 40 (13) ◽  
pp. 3356-3361 ◽  
Author(s):  
S. Y. Li ◽  
S. F. Zhang ◽  
H. Cai ◽  
X. H. Deng ◽  
X. Q. Chen ◽  
...  
Keyword(s):  
Solitary Waves ◽  
Three Dimensional ◽  
Bow Shock
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