TY - JOUR
T1 - Solitonic asymptotics for the Korteweg-de Vries equation in the small dispersion limit
JF - SIAM J. Math. Anal. 42 (2010) 2132-2154
Y1 - 2010
A1 - Tamara Grava
A1 - Tom Claeys
AB - 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.
UR - http://hdl.handle.net/1963/3839
U1 - 488
U2 - Mathematics
U3 - Mathematical Physics
ER -