期刊
SIAM JOURNAL ON MATHEMATICAL ANALYSIS
卷 42, 期 5, 页码 2132-2154出版社
SIAM PUBLICATIONS
DOI: 10.1137/090779103
关键词
Korteweg-de Vries; Riemann-Hilbert; small dispersion; soliton
资金
- ERC
- Belgian Interuniversity Attraction Pole [P06/02]
- ESF
- PRIN
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.
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