00906nas a2200109   4500008004300000245009100043210006900134520052300203100001800726700001600744856003600760       2010                        en_Ud  00aSolitonic asymptotics for the Korteweg-de Vries equation in the small dispersion limit0 aSolitonic asymptotics for the Kortewegde Vries equation in the s3 aWe 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.1 aGrava, Tamara1 aClaeys, Tom  uhttp://hdl.handle.net/1963/3839