Wikipedia:Peer review/List of nonlinear ordinary differential equations/archive1

List of nonlinear ordinary differential equations

I've listed this article for peer review because I'd like to know how it could be improved in general, if there's any equations people think are missing, and because I'd like to maybe take this to featured list.

Thanks, Nerd1a4i (they/them) (talk) 07:07, 3 June 2024 (UTC)

Comments from Dedhert.Jr

@Nerd1a4i I think I can help, although I am still trying to understand how the peer review works (as well as FL). You may also see some examples in our FLs. Dedhert.Jr (talk) 09:10, 4 June 2024 (UTC)

Thank you; let me know what recommendations you have! I'm also not entirely sure I follow the guidelines on accessibility, especially in terms of tables, so any advice on that would be greatly appreciated as well. Nerd1a4i (they/them) (talk) 05:36, 5 June 2024 (UTC)

I'll try my best. Dedhert.Jr (talk) 07:07, 5 June 2024 (UTC)

Temporarily, I could only think about the lead that was too short. It needs an explanation: what are differential equations in mathematics (explain it understandably, per WP:TECHNICAL, what is the background or history of differential equations (make it briefly), what makes the difference between the linear ordinary differential and the non-linear one (try to explain it step by step based on the difficulty to all readers, making the audience to understand as I mentioned in the previous point, specifically per WP:ONEDOWN). Never forget that when you write all of the facts, you need to put some reliable sources; I recommend you avoid some sources like MathWorld, PlanetMath, and other non-books and non-journal sources. If you remain struggling to find which sources are reliable, you can ask WT:WPM. Dedhert.Jr (talk) 07:24, 5 June 2024 (UTC)

Thank you for this advice - I am surprised MathWorld is considered an unreliable source! I will go through and adjust these when I next have time. Do you think it needs any media (e.g. images of the Lorenz attractor, etc.)? Nerd1a4i (they/them) (talk) 06:40, 9 June 2024 (UTC)

I am aware some people may misunderstand because of my comments above about MathWorld, explicitly and directly pointing at something that according to them makes mine seem to be harsh. Furthermore, I meticulously can give the background of some discussion about it. Dedhert.Jr (talk) 09:26, 9 June 2024 (UTC)

Kusma

I will review this soon. Good general sources with long lists of differential equations are [1] and [2]. —Kusma (talk) 10:35, 21 June 2024 (UTC)

• This is a difficult topic to cover, given how vast the scope is. Thank you for tackling this!
• It would be good to give an introduction clearly defining the scope (what is a "differential equation", what makes it "nonlinear", what is the difference between ordinary differential equations and partial differential equations). The current list has both single equations and systems of equations. That is fine, but you should perhaps state that somewhere. There is also a system of infinitely many equations (Toda lattice). Almost all equations are local (no nonlocal operators are involved) except for the Cherwell-Wright equation, which is a delay equation. Usually the independent variable is a real number, but sometimes it is complex (Nahm equations).
• In the main table, notation is all over the place and never explained. Arbitrary functions are sometimes called $P(x)$ and $Q(x)$, sometimes $f_{o}(x),f_{1}(x),g_{o}(x),g_{1}(x)$ (why subscript "o" instead of a zero?), independent variable switches between x, t, z in the Mathematics section alone. Differentiation is sometimes with a dash $y'$, sometimes Leibniz notation ${\frac {dy}{dx}}$, sometimes Newton notation ${\dot {y}}$. Sometimes it is fine to use specific notation in a specific context, but there should be some attempt at unifying notation.
• In the Mathematics section, a lot of the "Application" cells do not mention any applications, just features of the ODE or remarks about it. Some of them, like "Class of differential equation which may sometimes be solved exactly" are so vague that they are essentially useless.
• As mentioned above, Cherwell-Wright is not an ODE.
• It would be nice to mention applications of the equations in Mathematics, especially the context in which they occur.
• The "Darboux equation" says it is a general case of the "Jacobi equation". However, the Darboux equation is first order and the equation of Jacobi fields (where Jacobi equation redirects to) is second order; perhaps there is a different Jacobi equation?
• The first "Euler's differential equation" is a rather lame stub that does not even explain why this particular (boring looking) example of a separable equation deserves a name. The source linked does not help.
• Loewner equation: is w a complex variable? should be mentioned
• Logistic equation and Lorenz attractor: why are these in the Mathematics section while other similar equations are not?
• Nahm equations: notation very unexplained (this is a system of ODEs for a complex variable z, with values in matrices and using matrix commutators). The "applications" are more "fields of mathematics and physics where they occur".
• The Painleve transcendents: "Applications" are more a comment about their place in the history of mathematics than anything else
• Rabinovich–Fabrikant: why the different notation compared to Lorenz attractor?
• Equations I am missing here: geodesic equation, Jacobi field equation. There are probably more...
• Physics: Now notation gets really wild. In the pendulum equation, $\theta$ is an angle; what is it in the immediately following Poisson-Boltzmann equation (a temperature??)
• Some of these are 1D versions of partial differential equations; it is unclear where you draw the line for inclusion of those.
• The Heisenberg equation is not really an ODE; it is an ODE in an infinite-dimensional space that is equivalent to the Schrödinger equation, which we all agree is a PDE. Also it is linear, so it really has no place here.
• (Not checking all equations individually).
• Would suggest to drop the Toda lattice as including a single infinite-dimensional system opens all kinds of cans of worms for this list.
• Engineering: In this generality, is Liénard equation better here or in Mathematics? Same for the Rayleigh equation
• Biology and medicine: the first equation in Hodgkin-Huxley is not an ODE
• Price equation: the blackboard bold E for expectation value is not explained, and the notation with the underbraces explaining parts of the equation is nice, but only appears in this single equation

Overall there is a lot of work to do here. You need some good plan how to get through all of this, some better defined inclusion/exclusion criteria, some idea about notation, and some clarity on what you want to say about the equation (what is it applied to? in which fields of mathematics/physics/other things does it appear? how can it be solved? is there anything else interesting to say about it?). I am happy to clarify my comments above, but I won't be able to help much (if at all) with implementing them. Happy editing, —Kusma (talk) 11:34, 25 June 2024 (UTC)