@article {2007,
	title = {Numerical study of a multiscale expansion of KdV and Camassa-Holm equation},
	number = {arXiv.org;math-ph/0702038v1},
	year = {2007},
	abstract = {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},
	url = {http://hdl.handle.net/1963/2527},
	author = {Tamara Grava and Christian Klein}
}
