Talk:List of nonlinear partial differential equations

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I have undone the attempt to sort the equations for the following reasons:

• Many of the equations work in all dimensions and should not be sorted into particular dimensions
• It can be hard to tell whether a given equation is integrable or not; it seems better to label the individual equations for which this is known rather than try to sort them. (And several equations were misclassified). R.e.b. (talk) 20:30, 2 April 2008 (UTC)

[edit] Comments

Chiral field is a special case of the σ-model, and what is listed in the table as "σ model" is also just a special case of the latter. All the above are special cases of "minimal surfaces" or "harmonic maps", and may be defined in all dimensions (although only 1+1 is known to be "integrable"). The σ-model is just when the target space is a Riemannian symmetric space. A slight modification leads to the WZW (Wess-Zumino-Witten) model, which is important in conformal field theory.

The "eikonal equation" can occur in any (spatial) dimension and is, of course, a special case of the Hamilton-Jacobi equation. 24.202.238.172 (talk) 16:37, 6 April 2008 (UTC)

[edit] Further equations

Gauss-Codazzi equations (geometry / surfaces)

Garnier equations (isomonodromic deformations)

Witham equations (dispersionless limit / phase averaging) 132.205.67.123 (talk) 18:19, 3 April 2008 (UTC)