@article {2012,
	title = {The KdV hierarchy: universality and a Painleve transcendent},
	journal = {International Mathematics Research Notices, vol. 22 (2012) , page 5063-5099},
	number = {arXiv:1101.2602;},
	year = {2012},
	note = {This article was published in "International Mathematics Research Notices, vol. 22 (2012) , page 5063-5099},
	publisher = {Oxford University Press},
	abstract = {We study the Cauchy problem for the Korteweg-de Vries (KdV) hierarchy in the small dispersion limit where $\e\to 0$. For negative analytic initial data with a single negative hump, we prove that for small times, the solution is approximated by the solution to the hyperbolic transport equation which corresponds to $\e=0$. Near the time of gradient catastrophe for the transport equation, we show that the solution to the KdV hierarchy is approximated by a particular Painlev\'e transcendent. This supports Dubrovins universality conjecture concerning the critical behavior of Hamiltonian perturbations of hyperbolic equations. We use the Riemann-Hilbert approach to prove our results.},
	keywords = {Small-Dispersion limit},
	url = {http://hdl.handle.net/1963/6921},
	author = {Tom Claeys and Tamara Grava}
}
