01113nas a2200133   4500008004100000245006400041210005900105260002800164520069000192653002700882100001600909700001800925856003600943       2012                        en  d00aThe KdV hierarchy: universality and a Painleve transcendent0 aKdV hierarchy universality and a Painleve transcendent  bOxford University Press3 aWe 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.10aSmall-Dispersion limit1 aClaeys, Tom1 aGrava, Tamara  uhttp://hdl.handle.net/1963/6921