Talk:Dym equation

Alternative formulation?
The Dym equation



u_t = u^3u_{xxx} $$

appears to be written in many places as


 * $$u_t=(u^{-1/2})_{xxx}$$

and it is claimed for example in



that the two forms are equivalent. Can an expert confirm that? Oleg Alexandrov (talk) 04:10, 26 January 2007 (UTC)


 * Well, Peter Olver is an &uuml;berexpert so his word is law, but for your edification: Substitute $$ u = v^{-1/2} $$ in $$ u_t = v^3u_{xxx} $$ to get $$ (v^{-1/2})_t = v^{-3/2} (v^{-1/2})_{xxx} $$ and do the differentiation with respect to t to get $$ -(1/2) v_t = (v^{-1/2})_{xxx} $$. Finally, do some rescaling to get rid of the factor $$ -1/2 $$; for instance, set $$v(t,x) = w(-(1/2)t,x) $$. Any mistakes in my computations are left as an exercise for the reader. -- Jitse Niesen (talk) 08:40, 26 January 2007 (UTC)


 * Thanks! Frankly I was not expecting an answer to the above, it was more of a note to myself. (but big brother Jitse is watching. :)


 * I added the alternative formulation in the article (that one, $$u_t=(u^{-1/2})_{xxx}$$ is actually used much more often from what I saw in my google books search). If you have more to add to the article, you are more than welcome to. Oleg Alexandrov (talk) 16:47, 26 January 2007 (UTC)

Harry-Dym equation
Is this the same thing as the Harry-Dym equation, or is that something else? 67.198.37.16 (talk) 22:48, 16 September 2020 (UTC)