most recent 30 from http://mathoverflow.net 2013-05-23T06:14:41Z http://mathoverflow.net/feeds/user/23214 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/95209/rational-functions-on-2nd-order-pdes dirafu 2012-04-25T22:33:41Z 2012-04-26T11:33:51Z

<p>2nd order PDE are like conics but with differential equations instead of polynomials.</p> <p>Rational points on conics can be parameterized, but what about an analogous situation for solutions of a 2nd order PDE. </p> <p>Is there a parameterization of rational function solutions of a 2nd order PDE ?</p> <p>To get the analogy right, I think it is needed to have a linear 2nd order PDE in two variables with coefficients that are rational functions in rational numbers, and have the solutions parameterized by a rational function.</p> <p>So the parameterization of a PDE would be a function from the set of rational functions to the set of solutions that are rational functions.</p>