%0 Report
%D 2007
%T Numerical study of a multiscale expansion of KdV and Camassa-Holm equation
%A Tamara Grava
%A Christian Klein
%X We 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 equation
%G en_US
%U http://hdl.handle.net/1963/2527
%1 1591
%2 Mathematics
%3 Mathematical Physics
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