[Comportement asymptotique en temps grand de l’équation de Degasperis–Procesi sur la demi-droite]
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 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 -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.
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Keywords: Degasperis–Procesi equation, long-time asymptotics, Riemann–Hilbert problem, boundary value problem
Mot clés : Équation de Degasperis–Procesi, asymptotique en temps grand, problème de Riemann–Hilbert, problème aux limites.
@article{AIF_2019__69_1_171_0,
author = {Boutet de Monvel, Anne and Lenells, Jonatan and Shepelsky, Dmitry},
title = {Long-time asymptotics for the {Degasperis{\textendash}Procesi} equation on the half-line},
journal = {Annales de l'Institut Fourier},
pages = {171--230},
publisher = {Association des Annales de l{\textquoteright}institut Fourier},
volume = {69},
number = {1},
year = {2019},
doi = {10.5802/aif.3241},
language = {en},
url = {http://www.numdam.org/articles/10.5802/aif.3241/}
}
TY - JOUR AU - Boutet de Monvel, Anne AU - Lenells, Jonatan AU - Shepelsky, Dmitry TI - Long-time asymptotics for the Degasperis–Procesi equation on the half-line JO - Annales de l'Institut Fourier PY - 2019 SP - 171 EP - 230 VL - 69 IS - 1 PB - Association des Annales de l’institut Fourier UR - http://www.numdam.org/articles/10.5802/aif.3241/ DO - 10.5802/aif.3241 LA - en ID - AIF_2019__69_1_171_0 ER -
%0 Journal Article %A Boutet de Monvel, Anne %A Lenells, Jonatan %A Shepelsky, Dmitry %T Long-time asymptotics for the Degasperis–Procesi equation on the half-line %J Annales de l'Institut Fourier %D 2019 %P 171-230 %V 69 %N 1 %I Association des Annales de l’institut Fourier %U http://www.numdam.org/articles/10.5802/aif.3241/ %R 10.5802/aif.3241 %G en %F AIF_2019__69_1_171_0
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, Tome 69 (2019) no. 1, pp. 171-230. doi : 10.5802/aif.3241. http://www.numdam.org/articles/10.5802/aif.3241/
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