[Solitons et comportement en grand temps des solutions d’une équation multidimensionnelle intégrable]
L’équation de Novikov-Veselov est un analogue (2+1)-dimensionnel de l’équation classique de Korteweg-de Vries, intégrable via la transformation de diffusion inverse pour l’équation de Schrödinger bidimensionnelle stationnaire. Dans cet exposé on présente quelques résultats récents sur l’existence et l’absence de solitons algébriquement localisés pour l’équation de Novikov-Veselov ainsi que quelques résultats sur le comportement en grand temps des “inverse scattering” solutions de cette équation.
Novikov-Veselov equation is a (2+1)-dimensional analog of the classic Korteweg-de Vries equation integrable via the inverse scattering translform for the 2-dimensional stationary Schrödinger equation. In this talk we present some recent results on existence and absence of algebraically localized solitons for the Novikov-Veselov equation as well as some results on the large time behavior of the “inverse scattering solutions” for this equation.
Keywords: Novikov-Veselov equation, inverse scattering method, two-dimensional Schrödinger equation, solitons, large time behavior
Mot clés : équation de Novikov-Veselov, méthode de diffusion inverse, équation de Schrödinger bidimensionnelle, solitons, comportement en grand temps
@incollection{JEDP_2013____A6_0,
author = {Anna Kazeykina},
title = {Solitons and large time behavior of solutions of a multidimensional integrable equation},
booktitle = {},
series = {Journ\'ees \'equations aux d\'eriv\'ees partielles},
eid = {6},
pages = {1--17},
publisher = {Groupement de recherche 2434 du CNRS},
year = {2013},
doi = {10.5802/jedp.102},
language = {en},
url = {https://proceedings.centre-mersenne.org/articles/10.5802/jedp.102/}
}
TY - JOUR AU - Anna Kazeykina TI - Solitons and large time behavior of solutions of a multidimensional integrable equation JO - Journées équations aux dérivées partielles PY - 2013 SP - 1 EP - 17 PB - Groupement de recherche 2434 du CNRS UR - https://proceedings.centre-mersenne.org/articles/10.5802/jedp.102/ DO - 10.5802/jedp.102 LA - en ID - JEDP_2013____A6_0 ER -
%0 Journal Article %A Anna Kazeykina %T Solitons and large time behavior of solutions of a multidimensional integrable equation %J Journées équations aux dérivées partielles %D 2013 %P 1-17 %I Groupement de recherche 2434 du CNRS %U https://proceedings.centre-mersenne.org/articles/10.5802/jedp.102/ %R 10.5802/jedp.102 %G en %F JEDP_2013____A6_0
Anna Kazeykina. Solitons and large time behavior of solutions of a multidimensional integrable equation. Journées équations aux dérivées partielles (2013), article no. 6, 17 p. doi : 10.5802/jedp.102. https://proceedings.centre-mersenne.org/articles/10.5802/jedp.102/
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