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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]
Boutet de Monvel, Anne1 ; Lenells, Jonatan2 ; Shepelsky, Dmitry3
1 Institut de Mathématiques de Jussieu-PRG Université Paris Diderot 75205 Paris Cedex 13 (France)
2 Department of Mathematics KTH Royal Institute of Technology 10044 Stockholm (Sweden)
3 Mathematical Division Institute for Low Temperature Physics 61103 Kharkiv (Ukraine) and School of Mathematics and Computer Sciences V. N. Karazin Kharkiv National University 61022 Kharkiv (Ukraine)
Annales de l'Institut Fourier, Tome 69 (2019) no. 1, pp. 171-230.

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.

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Révisé le :
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DOI : 10.5802/aif.3241
Classification : 35Q53, 37K15
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.

Boutet de Monvel, Anne 1 ; Lenells, Jonatan 2 ; Shepelsky, Dmitry 3

1 Institut de Mathématiques de Jussieu-PRG Université Paris Diderot 75205 Paris Cedex 13 (France)
2 Department of Mathematics KTH Royal Institute of Technology 10044 Stockholm (Sweden)
3 Mathematical Division Institute for Low Temperature Physics 61103 Kharkiv (Ukraine) and School of Mathematics and Computer Sciences V. N. Karazin Kharkiv National University 61022 Kharkiv (Ukraine)
Licence : CC-BY-ND 4.0
Droits d'auteur : Les auteurs conservent leurs droits 
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     title = {Long-time asymptotics for the {Degasperis{\textendash}Procesi} equation on the half-line},
     journal = {Annales de l'Institut Fourier},
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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. https://aif.centre-mersenne.org/articles/10.5802/aif.3241/

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