All Questions
26
questions
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-...
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, ...
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 ...
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 ...
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 ...
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 ...
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 ...
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.
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?
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 ...