Non-linear dispersion of Stokes waves

1969 ◽  
Vol 3 (1) ◽  
pp. 45-54 ◽  
Author(s):  
H. W. Hoogstraten
Keyword(s):  
Linear Dispersion ◽  
Non Linear ◽  
Stokes Waves

scholarly journals 2- AND 3-DIMENSIONAL DETERMINISTIC FREAK WAVES

1982 ◽  
Vol 1 (18) ◽  
pp. 43
Author(s):  
Soren Peter Kjeldsen
Keyword(s):  
Dimensional Case ◽  
Linear Wave ◽  
Linear Dispersion ◽  
New Techniques ◽  
Freak Waves ◽  
3 Dimensional ◽  
Non Linear ◽  
Stokes Waves ◽  
First Results ◽  
Wave Trains

The present paper deals with a new non-linear technique for generation of violent breaking freak waves (plunging breakers) at specified positions and times in wave basins. First, results concerning generation of non-linear wave trains, Stokes-waves and wave solitons in deep water are given. Then the technique for generation of non-linear wave transients are given with specified non-linear dispersion properties. Finally, the new techniques are used to obtain collisions between non-linear solitons coming both from the same direction (2-dimensional case), and from different directions (3-dimensional case) leading to generation of steep and violent plunging breakers.

Non-linear transverse waves in a Vlasov plasma

1969 ◽  
Vol 3 (4) ◽  
pp. 577-592 ◽  
Author(s):  
S. Peter Gary
Keyword(s):  
Perturbation Expansion ◽  
Second Order ◽  
Electron Cyclotron ◽  
Wave Number ◽  
Linear Dispersion ◽  
Transverse Waves ◽  
Non Linear ◽  
Long Time ◽  
Linear Damping ◽  
Electron Cyclotron Waves

Non-linear transverse waves in a classical non-relativistic collisionless, Maxwellian electron gas with external magnetic field B0 are considered. There is assumed a small, sinusoidal variation in the initial electric and magnetic fields, corresponding to excitation of a discrete wave-number mode. The non-linear Vlasov equation is solved to second order in the long time limit via the Montgomery—Gorman perturbation expansion, and the time-independent, spatially homogeneous part of the second-order distribution function is used to modify the linear dispersion relation. For frequencies near the electron cyclotron frequency a non-linear damping decrement results such that, for many values of the parameters, the damping is less than the linear rate. Thus at sufficiently long times, the rate of damping of transverse electron cyclotron waves should decrease, a result similar to that for non-linear damping of longitudinal electron plasma waves.

Mild-slope solver including non-linear dispersion and bottom friction

2011 ◽  
Vol 49 (4) ◽  
pp. 547-553
Author(s):  
Jack Bokaris ◽  
Kostas Anastasiou
Keyword(s):  
Bottom Friction ◽  
Linear Dispersion ◽  
Non Linear

scholarly journals Shock waves and compactons for fifth-order non-linear dispersion equations

2009 ◽  
Vol 21 (1) ◽  
pp. 1-50 ◽  
Author(s):  
VICTOR A. GALAKTIONOV
Keyword(s):  
Entropy Solution ◽  
Travelling Wave ◽  
Linear Dispersion ◽  
Dispersion Equations ◽  
Non Linear ◽  
The Cauchy Problem ◽  
Order Degenerate ◽  
Image Position ◽  
Fifth Order ◽  
Degenerate Partial Differential Equations

The followingfirst problemis posed:is a correct ‘entropy solution’ of the Cauchy problem for the fifth-order degenerate non-linear dispersion equations (NDEs), same as for the classic Euler oneut+uux= 0,These two quasi-linear degenerate partial differential equations (PDEs) are chosen as typical representatives; so other (2m+ 1)th-order NDEs of non-divergent form admit such shocks waves. As a relatedsecond problem, the opposite initial shockS+(x) = −S−(x) = signxis shown to be a non-entropy solution creating ararefaction wave, which becomesC∞for anyt> 0. Formation of shocks leads to non-uniqueness of any ‘entropy solutions’. Similar phenomena are studied for afifth-order in timeNDEuttttt= (uux)xxxxinnormal form.On the other hand, related NDEs, such asare shown to admit smoothcompactons, as oscillatorytravelling wavesolutions with compact support. The well-known non-negative compactons, which appeared in various applications (first examples by Dey, 1998,Phys. Rev.E, vol. 57, pp. 4733–4738, and Rosenau and Levy, 1999,Phys. Lett.A, vol. 252, pp. 297–306), are non-existent in general and are not robust relative to small perturbations of parameters of the PDE.

scholarly journals Novel solitary wave solutions in parabolic law medium with weak non-local non-linearity

2021 ◽  
Vol 25 (Spec. issue 2) ◽  
pp. 239-246
Author(s):  
Mostafa Khater ◽  
Raghda Attia ◽  
Sayed Elagan ◽  
Meteub Alharthi
Keyword(s):  
Solitary Wave ◽  
Auxiliary Equation ◽  
Solitary Wave Solutions ◽  
Linear Dispersion ◽  
Auxiliary Equation Method ◽  
Wave Solutions ◽  
Parabolic Law ◽  
All Solutions ◽  
Non Linear ◽  
Non Local

In this paper, the auxiliary equation method is employed to construct novel solitary wave solutions of the dimensionless form of the non-linear Schrodinger equation with parabolic law of non-linearity in the presence of non-linear dispersion. The solutions are represented through various techniques to demonstrate the dynamical and physical behavior of the investigated models. All solutions are checked their accuracy by putting them back into the original model?s equation by MATHEMATICA 12.

scholarly journals Stimulated emission–based model of fast radio bursts

2020 ◽  
Vol 494 (1) ◽  
pp. 876-884 ◽  
Author(s):  
Mustafa Doğan ◽  
Kazım Yavuz Ekşi
Keyword(s):  
Electric Field ◽  
Radial Electric Field ◽  
Stimulated Emission ◽  
The Self ◽  
Radio Bursts ◽  
Linear Dispersion ◽  
Weibel Instability ◽  
Cylinder Radius ◽  
Light Cylinder ◽  
Non Linear

ABSTRACT Fast radio bursts (FRBs) are bright, short-duration radio transients with very high brightness temperatures implying highly coherent emission. We suggest that the FRBs are caused by the self-focusing of an electron beam interacting with an ambient plasma right beyond the light cylinder radius of a neutron star. The magnetic field at the light cylinder radius is relatively high that can accommodate both young Crab-like systems and old millisecond pulsars addressing the diverse environments of FRBs. At the first stage, the intense pulsed-beam passing through the background plasma causes instabilities such that the trapped particles in local Buneman-type cavitons saturate the local field. The beam is then radially self-focused due to the circular electric field developed by the two-stream instability that leads to Weibel instability in the transverse direction. Finally, the non-linear saturation of the Weibel instability results in the self-modulational formation of solitons due to plasmoid instability. The resonant solitary waves are the breather-type solitons hosting relativistic particles with self-excited oscillations. The analytical solutions obtained for non-linear dispersion and solitons suggest that, near the current sheets, the relativistic bunches are accelerated/amplified by klystron-like structures due to self-excited oscillations by the induced local electric field. Boosted coherent radio emission propagates through a narrow cone with strong focusing due to radial electric field and magnetic pinching. The non-linear evolution of solitons and the stimulated emission are associated with the Buneman instability and the possibility of the presence of nanosecond shots in FRBs are investigated.

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