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The '''Kaup–Kupershmidt equation''' (named after David J. Kaup and Boris Abram Kupershmidt) is the [[nonlinear]] fifth-order [[partial differential equation]]
This is a preview for the new '''MathML rendering mode''' (with SVG fallback), which is availble in production for registered users.


:<math>u_t = u_{xxxxx}+10u_{xxx}u+25u_{xx}u_x+20u^2u_x = \frac16 (6u_{xxxx}+60uu_{xx}+45u_x^2+40u^3)_x. </math>
If you would like use the '''MathML''' rendering mode, you need a wikipedia user account that can be registered here [[https://en.wikipedia.org/wiki/Special:UserLogin/signup]]
* Only registered users will be able to execute this rendering mode.
* Note: you need not enter a email address (nor any other private information). Please do not use a password that you use elsewhere.


It is the first equation in a hierarchy of [[integrable system|integrable equations]] with [[Lax pair|Lax operator]]
Registered users will be able to choose between the following three rendering modes:


:<math> \partial_x^3 + 2u\partial_x + u_x, </math> .
'''MathML'''
:<math forcemathmode="mathml">E=mc^2</math>


Ii has properties similar (but not identical) to those of the better-known [[Korteweg–de Vries equation|KdV hierarchy]] in which the Lax operator has order 2.
<!--'''PNG'''  (currently default in production)
{{Gallery
:<math forcemathmode="png">E=mc^2</math>
|width=250
|height=200
|align=center
|File:Kaup Kupershmidt JacobiSN method animation2.gif|Kaup Kupershmidt JacobiSN method bell solition animation2
|File:Kaup Kupershmidt JacobiSN method animation3.gif|Kaup Kupershmidt JacobiSN method bell soliton animation3
|File:Kaup Kupershmidt JacobiSN method animation4.gif|Kaup Kupershmidt JacobiSN method bell soloton  animation4
|File:Kaup Kupershmidt csch method animation2.gif|Kaup Kupershmidt csch method animation2
|File:Kaup Kupershmidt csch method animation3.gif|Kaup Kupershmidt csch method animation3
|File:Kaup Kupershmidt csch method animation5.gif|Kaup Kupershmidt csch method animation5
|File:Kaup Kupershmidt sec method animation3.gif|Kaup Kupershmidt sec method animation3
|File:Kaup Kupershmidt sec method animation5.gif|Kaup Kupershmidt sec method animation5
|File:Kaup Kupershmidt sec method animation10.gif|Kaup Kupershmidt sec method animation10
|File:Kaup Kupershmidt sech method animation2.gif|Kaup Kupershmidt sech method animation2
|File:Kaup Kupershmidt sech method animation4.gif|Kaup Kupershmidt sech method animation4
|File:Kaup Kupershmidt sech method animation8.gif|Kaup Kupershmidt sech method animation8


'''source'''
:<math forcemathmode="source">E=mc^2</math> -->


<span style="color: red">Follow this [https://en.wikipedia.org/wiki/Special:Preferences#mw-prefsection-rendering link] to change your Math rendering settings.</span> You can also add a [https://en.wikipedia.org/wiki/Special:Preferences#mw-prefsection-rendering-skin Custom CSS] to force the MathML/SVG rendering or select different font families. See [https://www.mediawiki.org/wiki/Extension:Math#CSS_for_the_MathML_with_SVG_fallback_mode these examples].


==Demos==


}}
Here are some [https://commons.wikimedia.org/w/index.php?title=Special:ListFiles/Frederic.wang demos]:




== References ==
* accessibility:
* {{cite journal | first = Ashok | last = Das |author2=Ziemowit Popowicz | year = 2005 | title = A nonlinearly dispersive fifth order integrable equation and its hierarchy | journal = Journal of Nonlinear Mathematical Physics | volume = 12 | issue = 1 | pages = 105–117 | url = http://www.sm.luth.se/~norbert/home_journal/electronic/121art5.pdf | format = PDF | doi = 10.2991/jnmp.2005.12.1.9 }}
** Safari + VoiceOver: [https://commons.wikimedia.org/wiki/File:VoiceOver-Mac-Safari.ogv video only], [[File:Voiceover-mathml-example-1.wav|thumb|Voiceover-mathml-example-1]], [[File:Voiceover-mathml-example-2.wav|thumb|Voiceover-mathml-example-2]], [[File:Voiceover-mathml-example-3.wav|thumb|Voiceover-mathml-example-3]], [[File:Voiceover-mathml-example-4.wav|thumb|Voiceover-mathml-example-4]], [[File:Voiceover-mathml-example-5.wav|thumb|Voiceover-mathml-example-5]], [[File:Voiceover-mathml-example-6.wav|thumb|Voiceover-mathml-example-6]], [[File:Voiceover-mathml-example-7.wav|thumb|Voiceover-mathml-example-7]]
** [https://commons.wikimedia.org/wiki/File:MathPlayer-Audio-Windows7-InternetExplorer.ogg Internet Explorer + MathPlayer (audio)]
** [https://commons.wikimedia.org/wiki/File:MathPlayer-SynchronizedHighlighting-WIndows7-InternetExplorer.png Internet Explorer + MathPlayer (synchronized highlighting)]
** [https://commons.wikimedia.org/wiki/File:MathPlayer-Braille-Windows7-InternetExplorer.png Internet Explorer + MathPlayer (braille)]
** NVDA+MathPlayer: [[File:Nvda-mathml-example-1.wav|thumb|Nvda-mathml-example-1]], [[File:Nvda-mathml-example-2.wav|thumb|Nvda-mathml-example-2]], [[File:Nvda-mathml-example-3.wav|thumb|Nvda-mathml-example-3]], [[File:Nvda-mathml-example-4.wav|thumb|Nvda-mathml-example-4]], [[File:Nvda-mathml-example-5.wav|thumb|Nvda-mathml-example-5]], [[File:Nvda-mathml-example-6.wav|thumb|Nvda-mathml-example-6]], [[File:Nvda-mathml-example-7.wav|thumb|Nvda-mathml-example-7]].
** Orca: There is ongoing work, but no support at all at the moment [[File:Orca-mathml-example-1.wav|thumb|Orca-mathml-example-1]], [[File:Orca-mathml-example-2.wav|thumb|Orca-mathml-example-2]], [[File:Orca-mathml-example-3.wav|thumb|Orca-mathml-example-3]], [[File:Orca-mathml-example-4.wav|thumb|Orca-mathml-example-4]], [[File:Orca-mathml-example-5.wav|thumb|Orca-mathml-example-5]], [[File:Orca-mathml-example-6.wav|thumb|Orca-mathml-example-6]], [[File:Orca-mathml-example-7.wav|thumb|Orca-mathml-example-7]].
** From our testing, ChromeVox and JAWS are not able to read the formulas generated by the MathML mode.


== External links ==
==Test pages ==
* {{mathworld|urlname=KupershmidtEquation|title=Kupershmidt Equation}}


{{DEFAULTSORT:Kaup-Kupershmidt equation}}
To test the '''MathML''', '''PNG''', and '''source''' rendering modes, please go to one of the following test pages:
[[Category:Partial differential equations]]
*[[Displaystyle]]
*[[MathAxisAlignment]]
*[[Styling]]
*[[Linebreaking]]
*[[Unique Ids]]
*[[Help:Formula]]


 
*[[Inputtypes|Inputtypes (private Wikis only)]]
{{mathanalysis-stub}}
*[[Url2Image|Url2Image (private Wikis only)]]
==Bug reporting==
If you find any bugs, please report them at [https://bugzilla.wikimedia.org/enter_bug.cgi?product=MediaWiki%20extensions&component=Math&version=master&short_desc=Math-preview%20rendering%20problem Bugzilla], or write an email to math_bugs (at) ckurs (dot) de .

Latest revision as of 22:52, 15 September 2019

This is a preview for the new MathML rendering mode (with SVG fallback), which is availble in production for registered users.

If you would like use the MathML rendering mode, you need a wikipedia user account that can be registered here [[1]]

  • Only registered users will be able to execute this rendering mode.
  • Note: you need not enter a email address (nor any other private information). Please do not use a password that you use elsewhere.

Registered users will be able to choose between the following three rendering modes:

MathML

E=mc2


Follow this link to change your Math rendering settings. You can also add a Custom CSS to force the MathML/SVG rendering or select different font families. See these examples.

Demos

Here are some demos:


Test pages

To test the MathML, PNG, and source rendering modes, please go to one of the following test pages:

Bug reporting

If you find any bugs, please report them at Bugzilla, or write an email to math_bugs (at) ckurs (dot) de .

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