Talk:Korteweg–De Vries equation/Archive 1

This is an archive of past discussions about Korteweg–De Vries equation. Do not edit the contents of this page. If you wish to start a new discussion or revive an old one, please do so on the current talk page.

Archive 1

Soliton Solution

Purely an ease thing, but for the soliton solution, the easiest way to solve it is to integrate again using f' as an integration factor 128.232.237.41 (talk) 16:17, 14 February 2009 (UTC)

This corresponds with the kinetic and (cubic) potential energy interpretation indicated in the article: multiply the equation with f' and integrate again. -- Crowsnest (talk) 19:19, 14 February 2009 (UTC)

Homogeneity of a PDE and classification of KdV

The following statement does not make sense to me: "The equation is homogeneous of degree 5 if x has degree 1, φ has degree 2, and t has degree 3."

I agree that the KdV equation is homogene, but for another reason, namely: there is no expression on the right hand side of the pde. So my suggestion is to change the above mentioned line into: The equation is homogeneous - in the usual sense of partial differential equation - which means roughly that there is no (nontrivial) expression on the right hand side which does not involve the solution φ itself.

By contrast the inhomogeneous version of the KdV equation looks like

\partial _{t}\phi +\partial _{x}^{3}\phi +6\,\phi \,\partial _{x}\phi =g(x,t),\,

with a known function g(x,t) depending only on x and t on the right hand side.

Some further words about classification: KdV is a third order, semilinear equation. By the way: Is the equation hyperbolic? —Preceding unsigned comment added by Aklaiber (talk • contribs) 20:37, 12 August 2009 (UTC)

Standard form

The standard form of the Korteweg-de Vries equation is ${\frac {\partial u}{\partial t}}-6u{\frac {\partial u}{\partial x}}+{\frac {\partial ^{3}u}{\partial t^{3}}}=0$ , and not the one given. —Preceding unsigned comment added by 64.198.242.52 (talk • contribs) 21:37, 5 November 2004

Except, that the dispersive term should be differentiated with respect to x.

${\frac {\partial u}{\partial t}}-6u{\frac {\partial u}{\partial x}}+{\frac {\partial ^{3}u}{\partial x^{3}}}=0$

—Preceding unsigned comment added by 137.205.162.8 (talk • contribs) 17:16, 6 September 2005

That is surely a matter of taste. At least in his textbook Partial Differential Equations (2002) Evans uses the version with $+$ sign as written in the article.

Aklaiber (talk) 20:42, 12 August 2009 (UTC)

External links modified

Hello fellow Wikipedians,

I have just modified 2 external links on Korteweg–de Vries equation. Please take a moment to review my edit. If you have any questions, or need the bot to ignore the links, or the page altogether, please visit this simple FaQ for additional information. I made the following changes:

When you have finished reviewing my changes, you may follow the instructions on the template below to fix any issues with the URLs.

This message was posted before February 2018. After February 2018, "External links modified" talk page sections are no longer generated or monitored by InternetArchiveBot. No special action is required regarding these talk page notices, other than regular verification using the archive tool instructions below. Editors have permission to delete these "External links modified" talk page sections if they want to de-clutter talk pages, but see the RfC before doing mass systematic removals. This message is updated dynamically through the template {{source check}} (last update: 5 June 2024).

If you have discovered URLs which were erroneously considered dead by the bot, you can report them with this tool.
If you found an error with any archives or the URLs themselves, you can fix them with this tool.

Cheers.—InternetArchiveBot (Report bug) 11:34, 12 December 2017 (UTC)

Does anyone interested in the article written by Korteweg & de Vries ?

I am reading the article and have some questions(see picture)

File:PBNX((3B)567) `FXBS )J9.png

I can't find the two formula in fulid mechanics .I need help,I need the answer ,Thank you— Preceding unsigned comment added by Davi689 (talk • contribs) 06:25, 24 April 2018 (UTC)

Connection to waves

A nice addition would be motivation of the KdV equation from physical principles (a 'derivation' of the wave equation). Does this exist? Chris2crawford (talk) 23:17, 8 November 2019 (UTC)

Sign error?

I think the equation should be (with a +6 rather than -6):

${\frac {\partial u}{\partial t}}+6u{\frac {\partial u}{\partial x}}+{\frac {\partial ^{3}u}{\partial x^{3}}}=0$

This seems to be the case in the following two references:

[1] https://journals.aps.org/prl/pdf/10.1103/PhysRevLett.15.240

[2] https://www.pnas.org/content/pnas/suppl/2019/07/15/1814058116.DCSupplemental/pnas.1814058116.sapp.pdf (Equation S4)

Can anyone explain this? Perhaps it should be included in the page as well for newcomers to this field (such as myself).— Preceding unsigned comment added by G-d (talk • contribs) 23:55, 31 July 2021 (UTC)