Timeline for Can a "depressive soliton" wave exist? That is, can we have a trough without any crest? Why or why not?
Current License: CC BY-SA 4.0
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| Jun 17, 2023 at 19:49 | comment | added | hyportnex | From the very deep past what I can recall is that the issue is related to the fact the higher the wave the faster it is, thus a depression cannot be stable. This you can see by neglecting the dispersive term represented by the 3rd derivative $u_{xxx}$ and by writing the remainder of the KdV as $u_t+uu_x$ whose solution is $u=f(s)$ with $s=x-ut$ for any differentiable $f(s)$. This shows that the apparent nondispersive wave speed is $u$. In a trough the surrounding is always at a higher speed than the trough itself, so it cannot be stable. | |
| Jun 17, 2023 at 16:35 | history | reopened |
hyportnex MaximusIdeal John Doty |
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| Jun 17, 2023 at 16:05 | history | edited | MaximusIdeal | CC BY-SA 4.0 |
Added citation, added tags, improved title
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| Jun 17, 2023 at 14:16 | comment | added | hyportnex | This is a good question and its answer is nontrivial. | |
| Jun 17, 2023 at 14:15 | review | Reopen votes | |||
| Jun 17, 2023 at 16:37 | |||||
| Jun 17, 2023 at 14:12 | history | closed |
anna v Miyase Jon Custer |
Needs details or clarity | |
| Jun 17, 2023 at 7:18 | comment | added | Farcher | A link to the Wikipedia article Dispersion (water waves) in section shallow water. | |
| Jun 17, 2023 at 5:40 | comment | added | FlatterMann | Can you give a citation to the specific language in that page? Did they say that equations that produce solitons can not have an almost everywhere nearly constant non-zero solution with a stable "dip" in them? | |
| Jun 17, 2023 at 4:20 | review | Close votes | |||
| Jun 17, 2023 at 14:12 | |||||
| Jun 17, 2023 at 2:41 | history | asked | Abdullah is not an Amalekite | CC BY-SA 4.0 |