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First integrals for nonlinear dispersive equations


Author: Frédéric Hélein
Journal: Trans. Amer. Math. Soc. 368 (2016), 6939-6978
MSC (2010): Primary 35C10, 35C20, 35L05, 35L70, 35Q53; Secondary 35L65, 41A58
DOI: https://doi.org/10.1090/tran/6573
Published electronically: November 12, 2015
MathSciNet review: 3471082
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Abstract: Given a solution of a semilinear dispersive partial differential equation with a real analytic nonlinearity, we relate its Cauchy data at two different times by nonlinear representation formulas in terms of convergent series. These series are constructed by means of generating functions. All of this theory is based on a new suitable formulation of the dynamics of solutions of dispersive equations.


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Frédéric Hélein
Affiliation: L’Institut de Mathématiques de Jussieu-Paris Rive Gauche (IMJ–PRG), UMR CNRS 7586, Paris Cedex 05, France – and – Bâtiment Sophie Germain, Université Paris Diderot, Case 7012, 75205 Paris Cedex 13, France
Email: helein@math.univ-paris-diderot.fr

DOI: https://doi.org/10.1090/tran/6573
Received by editor(s): August 20, 2014
Published electronically: November 12, 2015
Article copyright: © Copyright 2015 American Mathematical Society