All Questions
26
questions
0
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0
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30
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Overview work on radio solitons?
I've heard about solitons in dense mediums (water), sparse mediums (acoustic) and optical fiber.
But I can't find a good overview work on solitons in radio spectrum. Something like generating EM ...
- 111
7
votes
0
answers
109
views
Can a "depressive soliton" wave exist? That is, can we have a trough without any crest? Why or why not?
I know that "soliton" waves can consist of a crest without a trough. One would expect the reverse to be true as well.
However, this Wikipedia excerpt says,
So for this nonlinear gravity ...
1
vote
0
answers
46
views
Wave propagation speed in non-linear differential equations
Could it happen than a solitary travelling wave (soliton) had a different propagation speed when seen from the usual wave equations from that in a non-linear equation. I mean, suppose a solution $F=f(...
- 6,611
0
votes
2
answers
53
views
Does a general soliton solution satisfy ALSO the normal wave equation?
I checked that the usual wave funtions of a gaussian pulse, a $\text{sech}(x-vt)$ and $\text{sech}^2(x-vt)$ solitons (the two latter from KdV equations) satisfy the wave equation.
Is this general? I ...
- 6,611
2
votes
2
answers
144
views
Wave without trough?
Why does this video appear to show a wave with no trough? Do such waves exist?
2
votes
0
answers
27
views
Questions on the Zakharov-Shabat inverse scattering paper
I am trying to work through the Zakharov and Shabat paper on inverse scattering for the nonlinear Schrodinger equation (PDF). I am stuck on section 2.
Problem 1. I need to know how to reconstruct $\...
- 51
2
votes
0
answers
33
views
Can "solitons" be explained by linear wave equation? [duplicate]
In this Wikipedia page about the history of solitons, the author say that the observations made by Scott Russell "could not be explained by the existing water wave theories" at that time.
...
- 1,335
2
votes
2
answers
327
views
Are cross sea waves solitons?
Last week I went to the sea and observed some waves of the type pictured here
By Michel Griffon - Own work, CC BY 3.0, Link
And I wondered if they were solitons or not. I've seen more than once ...
- 43
0
votes
1
answer
848
views
Soliton solution of the NLS equation
My understanding of soliton - it is a moving pulse in a medium which does not change its structure with time. It has other properties like no interaction with other solitons (this could certainly be ...
- 484
0
votes
1
answer
126
views
Periodic traveling waves of the form $\phi(x,t)=\psi_c(x-ct)$ for a $\phi^4$ model
Consider
\begin{equation}\label{1}
\partial^2_t\phi-\partial^2_x\phi=\phi -\phi^3,\: \ (x,t) \in \mathbb{R}\times \mathbb{R} \hspace{30pt}(1)
\end{equation}
the $\phi^4$ model.
I know that
$$H(x)=\...
- 103
19
votes
4
answers
5k
views
Will tsunami waves travel forever if there was no land?
If there was no land for tsunami waves to collide with, can the waves travel around the globe for forever?
- 329
1
vote
0
answers
20
views
Can inhomogeneity in the medium accelerate particles
Suppose I have a charge which is moving in through a medium with constant velocity. Now, what will happen to the charge as it encounters an inhomogeneity in density? whether it will accelerate or ...
1
vote
1
answer
372
views
What does the motion of water in tsunamis look like?
This is what normal wave motion looks like.
Do tsunamis that travel at 60mph look any different?
- 6,044
8
votes
1
answer
368
views
KdV suggests a connection between waves in shallow water and the potential in the Schrödinger equation. What is the intuitive explanation?
The KdV equation
$$v_t+\frac{1}{4}v_{xxx}-\frac{3}{2}vv_x=0$$
was originally invented to model waves in shallow water.
However, it is well known that it also has applications in quantum mechanics. ...
- 183
2
votes
3
answers
548
views
Describing travelling waves carrying energy from one point to another
A simple harmonic wave in one-dimension (for simplicity) $y(x,t)=A\sin(\omega t-kx)$ in a medium is often presented as an example of a travelling wave. But such a plane wave is infinitely extended ...
- 26.8k
4
votes
0
answers
102
views
Characteristics of wavepackets
I've been learning about wave packets and group velocities recently and had a question. Using simple trigonometric identies, we can show that the super position of two traveling waves with frequency-...
- 41
5
votes
2
answers
2k
views
Do plane waves exist in nature? [duplicate]
Drop a stone in the pond...a wave propagates radially from the source. The conservation of energy says the wave must decay proportionally to the radial distance. If I drop a steel I-beam in the pond, ...
- 160
1
vote
0
answers
107
views
Nonlinear Saturated Schrodinger Equation in 1D- Physical Models
I'm studying the Nonlinear 1d Schrodinger equation
$$i\psi _t + \psi '' + |\psi |^{2p} \psi - \epsilon |\psi | ^{2q} \psi = 0\, , \quad t>0, x\in \mathbb{R}\, ,$$
and specifically, its solitary ...
- 153
3
votes
2
answers
67
views
Can localized fluid perturbations be accelerated by pressure gradients?
I would like to know if there are any examples in fluid dynamics (or continuum dynamics) of small perturbations (or waves, solitons, or other "localized" solutions of the fluid) being accelerated in ...
- 340
2
votes
1
answer
89
views
Solitons and its infinite extension
A soliton, for example the KdV equation solution, has the profile proportional to a hyperbolic secant squared ${\text{sech}}^{2}(x-ct)$. And since it is hyperbolic it has an exponential dependence, so ...
- 171
5
votes
2
answers
204
views
Besides vortex rings, are there other types of traveling waves that can carry matter as well as energy?
Vortex rings are a special soliton wave that are known to carry matter over a distance as well as energy. This can easily be demonstrated using a cardboard 'vortex canon' filled with smoke. The smoke ...
- 11.7k
12
votes
2
answers
7k
views
Explanation of the waves on the water planet in the movie Interstellar?
We will ignore some of the more obvious issues with the movie and assume all other things are consistent to have fun with some of these questions.
Simple [hopefully] Pre-questions:
1) If the water ...
- 15.6k
0
votes
1
answer
212
views
Speed of an electromagnetic soliton in free space
What is the speed of an electromagnetic soliton in free space? Is it equal to 'c' ?
P.S. My understanding of the Fourier transform says it's not.
- 1,258
2
votes
0
answers
244
views
Phase and group velocity of a soliton? [closed]
How do I find the phase velocity and group velocity of a soliton with a $\operatorname{sech}$ (hyperbolic secant) envelope?
- 151
1
vote
0
answers
185
views
Is there a consensus on the definition of wavelength for a solitary wave?
Solitary waves are by definition a wave of single nature so the usual definition for periodic waves does not apply. R. Dalrymple provides a definition but I saw a lot of other websites and papers ...
4
votes
1
answer
360
views
Why linear wave equation does not have solitonic solutions?
As many people define solitary waves they are localized pulses that propagate without changing the shape. As far as I know the same pulses exist in ordinary wave equation ! why should we look for ...
- 4,194