Talk:Integrable system

message: I'm a physics student, and I'm not familiar with the level of mathematics that is discussed in this article, but my understanding of integrable systems is this: if the phase space is 2n dimensional, there should be n independent conserved quantities which are in involution, ie, their Poisson brackets separately vanish. This means that the phase space is confined to a surface that is homeomorphic to an n-torus. It also means that their equations of motion can be reduced to quadratures and can in principle be solved by a sequence of integrals. I think this is the basic definition that most physicists would look for, and it is really, really hard to make that out from this article. I don't feel confident editing it, because I don't understand half the math terms involved. But it would be nice if someone who does could tone it down a bit. SrijitaK (talk) 18:23, 21 February 2012 (UTC)
replies: text: I completely agree! This is way too mathematical. wpoely86 (talk) 10:05, 2 July 2012 (UTC)

text: In fact, this page is completely unreadable. I just want to know what it means for a system to be integrable, and this article is completely useless to 99% of people. Dragonfiremalus (talk) 20:11, 14 December 2013 (UTC)
replies: text: Also agree the article is utterly incomprehensible to a layperson. I would forgive its opaqueness to the average reader if it simply began with a single short sentence that says: "An integrable system in mathematics is one in which < finish the sentence by describing the basic concept in ordinary English without using any technical terms nor referring to the names of particular systems >."   Hypothetical example: "...one in which certain equations can be completely solved by conventional algebra." (This is merely an example of the use of easily understood English; it is not a suggestion for the actual wording, which I'm not qualified to offer.) It seems to me that any qualified mathematician, after giving the matter some thought, should be able to write an opening sentence that can be understood by anyone and does not rely on textbook jargon. DonFB (talk) 01:48, 12 June 2018 (UTC)
replies: text: This is an arcane, highly technical and difficult branch of mathematics, requiring years of background study. Why, exactly, are you interested in reading this article, and what do you hope to get out of it? What brought you to this article? What did you hope to learn?  (Yes, people want to read about black holes and quantum mechanics, but without the formulas; but is this also the case for integrable systems? Surely not. So then what?) 67.198.37.16 (talk) 23:30, 9 January 2019 (UTC)
thread_title:  Too technical 

message: It would be useful to add a counter-example to the article, i.e. a simple example that is *not* integrable.   18.87.1.116 (talk) 16:35, 3 February 2016 (UTC)
replies: text: An automobile driven on a flat surface is non-integrable. You can drive it anywhere you want. Compare and contrast to a roller-coaster at an amusement park, which is integrable.67.198.37.16 (talk) 23:57, 9 January 2019 (UTC)
thread_title:  A counter-example would be useful 

message: Substituted at 18:59, 29 April 2016 (UTC)
thread_title: Assessment comment

message: In the preceding discussion and in some versions of the lead, it seems that there is some confusion between integral and integrable. For this reason, I have added a hatnote to the article, and removed the link to integral.
In fact, here, integration and integrable have nothing to do with integral: in the jargon of differential equations, "integrating" means "solving from given initial conditions". This should be said somewhere in Wikipedia, but I have not found where. 
Thinking again to the problem, I'll add a footnote to the article, and an entry in Integration (disambiguation). D.Lazard (talk) 09:46, 13 June 2018 (UTC)
replies: text: I have also edited Integration (disambiguation) for disambiguating between these two notions of integration. D.Lazard (talk) 19:52, 13 June 2018 (UTC)
thread_title:  Integration: integrable vs. integral 

message: In my judgement the lead is massively improved in readability, but it is decisive for removing the relevant banner, if the article is now perceived also by others as sufficiently accessible, resp., if there are still wordings suggested for an urgent improvement. I take the freedom to ping . Purgy (talk) 07:22, 14 June 2018 (UTC)
replies: text: I don't oppose removal of the Incomprehensible tag, which I added in the first place. Parts of the article remain incomprehensible to me, but I'm not a mathematician. DonFB (talk) 07:26, 14 June 2018 (UTC)
replies: text: I think the tag is still appropriate, for what it's worth.  The lead might be comprehensible (but at the expense of not really saying much), but the article itself is pretty incomprehensible.  Sławomir Biały (talk) 10:26, 14 June 2018 (UTC)
replies: text: Small strengthening: The first paragraph of the lead might be comprehensible (but at the expense of not really saying much), but the article itself is pretty incomprehensible, even for an experimented mathematician. D.Lazard (talk) 10:51, 14 June 2018 (UTC)

text: Moreover, the linked articles do not help understanding, because they suffer from the same issues. D.Lazard (talk) 10:55, 14 June 2018 (UTC)
thread_title:  Incomprehensibility 

message: Some more models solved via inverse-scattering:
* Reduced Maxwell-Bloch equation
* Self-induced-transparency (SIT) equation
* Coupled non-linear Schrodinger equation
67.198.37.16 (talk) 22:55, 16 September 2020 (UTC)
thread_title:  TODO