@article {2010,
title = {Solitonic asymptotics for the Korteweg-de Vries equation in the small dispersion limit},
journal = {SIAM J. Math. Anal. 42 (2010) 2132-2154},
number = {SISSA;09/2010/FM},
year = {2010},
abstract = {We study the small dispersion limit for the Korteweg-de Vries (KdV) equation $u_t+6uu_x+\\\\epsilon^{2}u_{xxx}=0$ in a critical scaling regime where $x$ approaches the trailing edge of the region where the KdV solution shows oscillatory behavior. Using the Riemann-Hilbert approach, we obtain an asymptotic expansion for the KdV solution in a double scaling limit, which shows that the oscillations degenerate to sharp pulses near the trailing edge. Locally those pulses resemble soliton solutions of the KdV equation.},
doi = {10.1137/090779103},
url = {http://hdl.handle.net/1963/3839},
author = {Tamara Grava and Tom Claeys}
}