Long-time asymptotics for the Degasperis–Procesi equation on the half-line  [ Comportement asymptotique en temps grand de l’équation de Degasperis–Procesi sur la demi-droite ]
Annales de l'Institut Fourier, à paraître, p. 1-60
Nous étudions le comportement asymptotique en temps grand de l’équation de Degasperis–Procesi sur la demi-droite. L’application de techniques de descente de plus grande pente non linéaire à un problème de Riemann–Hilbert matriciel 3×3 associé nous permet d’obtenir une formule explicite, en termes des données initiale et au bord, pour le terme dominant de l’asymptotique de la solution dans la région de similarité.
We analyze the long-time asymptotics for the Degasperis–Procesi equation on the half-line. By applying nonlinear steepest descent techniques to an associated 3×3-matrix valued Riemann–Hilbert problem, we find an explicit formula for the leading order asymptotics of the solution in the similarity region in terms of the initial and boundary values.
Reçu le : 2015-08-17
Révisé le : 2016-08-18
Accepté le : 2017-12-08
Classification:  35Q53,  37K15
Mots clés: Équation de Degasperis–Procesi, asymptotique en temps grand, problème de Riemann–Hilbert, problème aux limites.
@unpublished{AIF_0__0_0_A5_0,
     author = {Boutet de Monvel, Anne and Lenells, Jonatan and Shepelsky, Dmitry},
     title = {Long-time asymptotics for the Degasperis--Procesi equation on the half-line},
     note = {to appear in \emph{Annales de l'Institut Fourier}},
}
Boutet de Monvel, Anne; Lenells, Jonatan; Shepelsky, Dmitry. Long-time asymptotics for the Degasperis–Procesi equation on the half-line. Annales de l'Institut Fourier, à paraître, pp. 1-60.

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