TY - RPRT
T1 - Numerical study of a multiscale expansion of KdV and Camassa-Holm equation
Y1 - 2007
A1 - Tamara Grava
A1 - Christian Klein
AB - 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
UR - http://hdl.handle.net/1963/2527
U1 - 1591
U2 - Mathematics
U3 - Mathematical Physics
ER -