Two dimensional cylindrical fast magnetoacoustic solitary waves in a dust plasma

2011 ◽  
Vol 18 (4) ◽  
pp. 044501 ◽  
Keyword(s):  
Solitary Waves ◽  
Two Dimensional ◽  
Dust Plasma

Propagation of two dimensional cylindrical fast magnetoacoustic solitary waves in a warm dust plasma

2013 ◽  
Vol 347 (1) ◽  
pp. 139-143 ◽  
Author(s):  
Hai-Feng Liu ◽  
Shi-Qing Wang ◽  
Fa-Zhan Yang
Keyword(s):  
Solitary Waves ◽  
Two Dimensional ◽  
Dust Plasma

Comparison principles for free-surface flows with gravity

1991 ◽  
Vol 230 ◽  
pp. 231-243 ◽  
Author(s):  
Walter Craig ◽  
Peter Sternberg
Keyword(s):  
Solitary Waves ◽  
Finite Depth ◽  
Free Surface Flows ◽  
Immiscible Fluids ◽  
Steady Flows ◽  
Two Dimensional ◽  
Surface Flows ◽  
Ship Hulls ◽  
Geometrical Information ◽  
Supercritical Flows

This article considers certain two-dimensional, irrotational, steady flows in fluid regions of finite depth and infinite horizontal extent. Geometrical information about these flows and their singularities is obtained, using a variant of a classical comparison principle. The results are applied to three types of problems: (i) supercritical solitary waves carrying planing surfaces or surfboards, (ii) supercritical flows past ship hulls and (iii) supercritical interfacial solitary waves in systems consisting of two immiscible fluids.

scholarly journals The Asymptotic Approach to the Description of Two-Dimensional Symmetric Soliton Patterns

Symmetry ◽  
2020 ◽  
Vol 12 (10) ◽  
pp. 1586
Author(s):  
Yury Stepanyants
Keyword(s):  
Solitary Waves ◽  
Asymptotic Theory ◽  
Deep Ocean ◽  
Two Dimensional ◽  
Asymptotic Approach ◽  
Suggested Approach ◽  
Symmetric Wave ◽  
Petviashvili Equation ◽  
Wave Patterns ◽  
Symmetric Soliton

The asymptotic approach is suggested for the description of interacting surface and internal oceanic solitary waves. This approach allows one to describe stationary moving symmetric wave patterns consisting of two plane solitary waves of equal amplitudes moving at an angle to each other. The results obtained within the approximate asymptotic theory are validated by comparison with the exact two-soliton solution of the Kadomtsev–Petviashvili equation (KP2-equation). The suggested approach is equally applicable to a wide class of non-integrable equations too. As an example, the asymptotic theory is applied to the description of wave patterns in the 2D Benjamin–Ono equation describing internal waves in the infinitely deep ocean containing a relatively thin one of the layers.

scholarly journals On the Dynamics of Two-Dimensional Capillary-Gravity Solitary Waves with a Linear Shear Current

2014 ◽  
Vol 2014 ◽  
pp. 1-7 ◽  
Author(s):  
Dali Guo ◽  
Bo Tao ◽  
Xiaohui Zeng
Keyword(s):  
Solitary Waves ◽  
Gravity Waves ◽  
Small Amplitude ◽  
Numerical Study ◽  
Two Dimensional ◽  
Shear Current ◽  
Linear Shear ◽  
The Stability ◽  
Depression Wave ◽  
Elevation Wave

The numerical study of the dynamics of two-dimensional capillary-gravity solitary waves on a linear shear current is presented in this paper. The numerical method is based on the time-dependent conformal mapping. The stability of different kinds of solitary waves is considered. Both depression wave and large amplitude elevation wave are found to be stable, while small amplitude elevation wave is unstable to the small perturbation, and it finally evolves to be a depression wave with tails, which is similar to the irrotational capillary-gravity waves.

scholarly journals Transverse instability of gravity–capillary solitary waves on deep water in the presence of constant vorticity

2019 ◽  
Vol 871 ◽  
pp. 1028-1043
Author(s):  
M. Abid ◽  
C. Kharif ◽  
H.-C. Hsu ◽  
Y.-Y. Chen
Keyword(s):  
Growth Rate ◽  
Solitary Wave ◽  
Solitary Waves ◽  
Deep Water ◽  
Capillary Waves ◽  
Two Dimensional ◽  
Transverse Instability ◽  
Constant Vorticity ◽  
Dimensional Gravity ◽  
Wave Properties

The bifurcation of two-dimensional gravity–capillary waves into solitary waves when the phase velocity and group velocity are nearly equal is investigated in the presence of constant vorticity. We found that gravity–capillary solitary waves with decaying oscillatory tails exist in deep water in the presence of vorticity. Furthermore we found that the presence of vorticity influences strongly (i) the solitary wave properties and (ii) the growth rate of unstable transverse perturbations. The growth rate and bandwidth instability are given numerically and analytically as a function of the vorticity.

Head-on collision of dust magnetoacoustic solitary waves in magnetized plasmas

2013 ◽  
Vol 80 (2) ◽  
pp. 235-245 ◽  
Author(s):  
Shi-Sen Ruan ◽  
Zhong-Ming Li
Keyword(s):  
Solitary Waves ◽  
Magnetic Field Intensity ◽  
Acoustic Velocity ◽  
Number Density ◽  
Ion Temperature ◽  
Component Plasma ◽  
The Magnetic Field ◽  
Dust Surface ◽  
Dust Plasma ◽  
Alfven Velocity

AbstractThe head-on collision of dust magnetoacoustic solitary waves (DMASWs) is studied in magnetized electron–ion–dust plasma. The extended Poincaré–Lighthill–Kuo perturbation method is used to derive the Korteweg de Vries equations for DMASWs in this three-component plasma. The effects of the magnetic field intensity B0, the number of electrons residing on dust surface Zd, the ratio of electron to dust number density δ, the ratio of electron to ion temperature σ, and the ratio of dust acoustic velocity to dust Alfvén velocity β on the phase shift are investigated. It is found that these parameters can significantly influence the phase shifts of colliding DMASWs. The present investigation may be beneficial to understand the interaction between two DMASWs that may occur in plasma with dust impurities situations.

Asymptotic expansions for solitary gravity-capillary waves in two and three dimensions

2009 ◽  
Vol 465 (2109) ◽  
pp. 2725-2749 ◽  
Author(s):  
M. J. Ablowitz ◽  
T. S. Haut
Keyword(s):  
Surface Tension ◽  
Solitary Wave ◽  
Solitary Waves ◽  
Asymptotic Series ◽  
High Order ◽  
Three Dimensions ◽  
Two Dimensional ◽  
Small Surface ◽  
Petviashvili Equation ◽  
Dimensional Series

High-order asymptotic series are obtained for two- and three-dimensional gravity-capillary solitary waves. In two dimensions, the first term in the asymptotic series is the well-known sech 2 solution of the Korteweg–de Vries equation; in three dimensions, the first term is the rational lump solution of the Kadomtsev–Petviashvili equation I. The two-dimensional series is used (with nine terms included) to investigate how small surface tension affects the height and energy of large-amplitude waves and waves close to the solitary version of Stokes’ extreme wave. In particular, for small surface tension, the solitary wave with the maximum energy is obtained. For large surface tension, the two-dimensional series is also used to study the energy of depression solitary waves. Energy considerations suggest that, for large enough surface tension, there are solitary waves that can get close to the fluid bottom. In three dimensions, analytic solutions for the high-order perturbation terms are computed numerically, and the resulting asymptotic series (to three terms) is used to obtain the speed versus maximum amplitude curve for solitary waves subject to sufficiently large surface tension. Finally, the above asymptotic method is applied to the Benney–Luke (BL) equation, and the resulting asymptotic series (to three terms) is verified to agree with the solitary-wave solution of the BL equation.

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