01084nas a2200109   4500008004300000245007900043210006900122520070800191100001800899700002100917856003600938       2007                        en_Ud  00aNumerical study of a multiscale expansion of KdV and Camassa-Holm equation0 aNumerical study of a multiscale expansion of KdV and CamassaHolm3 aWe study numerically solutions to the Korteweg-de Vries and Camassa-Holm equation close to the breakup of the corresponding solution to the dispersionless equation. The solutions are compared with the properly rescaled numerical solution to a fourth order ordinary differential equation, the second member of the Painlev\\\\\\\'e I hierarchy. It is shown that this solution gives a valid asymptotic description of the solutions close to breakup. We present a detailed analysis of the situation and compare the Korteweg-de Vries solution quantitatively with asymptotic solutions obtained via the solution of the Hopf and the Whitham equations. We give a qualitative analysis for the Camassa-Holm equation1 aGrava, Tamara1 aKlein, Christian  uhttp://hdl.handle.net/1963/2527