%0 Journal Article
%J Comm. Math. Phys. 286 (2009) 979-1009
%D 2009
%T Universality of the break-up profile for the KdV equation in the small dispersion limit using the Riemann-Hilbert approach
%A Tamara Grava
%A Tom Claeys
%X We obtain an asymptotic expansion for the solution of the Cauchy problem for the Korteweg-de Vries (KdV) equation in the small dispersion limit near the point of gradient catastrophe (x_c,t_c) for the solution of the dispersionless equation.\\nThe sub-leading term in this expansion is described by the smooth solution of a fourth order ODE, which is a higher order analogue to the Painleve I equation. This is in accordance with a conjecture of Dubrovin, suggesting that this is a universal phenomenon for any Hamiltonian perturbation of a hyperbolic equation. Using the Deift/Zhou steepest descent method applied on the Riemann-Hilbert problem for the KdV equation, we are able to prove the asymptotic expansion rigorously in a double scaling limit.
%B Comm. Math. Phys. 286 (2009) 979-1009
%G en_US
%U http://hdl.handle.net/1963/2636
%1 1487
%2 Mathematics
%3 Mathematical Physics
%$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2008-04-22T10:17:48Z\\nNo. of bitstreams: 1\\n0801.2326v1.pdf: 375000 bytes, checksum: b00b6e0d823d47a002430b4fdecf8c7c (MD5)
%R 10.1007/s00220-008-0680-5