@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} }