Results on qualitative features of periodic solutions of KdV
T. Kappeler, B. Schaad, P. Topalov (2011-2012)
Séminaire Laurent Schwartz — EDP et applications
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T. Kappeler, B. Schaad, P. Topalov (2011-2012)
Séminaire Laurent Schwartz — EDP et applications
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Ricardo Pérez-Marco (2001-2002)
Séminaire Bourbaki
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Jean Bourgain (1998)
Publications Mathématiques de l'IHÉS
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Massimiliano Berti (2011-2012)
Séminaire Laurent Schwartz — EDP et applications
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The aim of this talk is to present some recent existence results about quasi-periodic solutions for PDEs like nonlinear wave and Schrödinger equations in , , and the - derivative wave equation. The proofs are based on both Nash-Moser implicit function theorems and KAM theory.
Daxin Wu, Shih-Liang Wen (1991)
Rendiconti del Seminario Matematico della Università di Padova
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Jerry L. Bona, Zoran Grujić, Henrik Kalisch (2005)
Annales de l'I.H.P. Analyse non linéaire
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Axel Grünrock (2010)
Open Mathematics
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The Cauchy problem for the higher order equations in the mKdV hierarchy is investigated with data in the spaces defined by the norm . Local well-posedness for the jth equation is shown in the parameter range 2 ≥ 1, r > 1, s ≥ . The proof uses an appropriate variant of the Fourier restriction norm method. A counterexample is discussed to show that the Cauchy problem for equations of this type is in general ill-posed in the C 0-uniform sense, if s < . The results for r =...