First integrals for nonlinear dispersive equations

Hélein, Frédéric

doi:10.1090/tran/6573

First integrals for nonlinear dispersive equations
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by Frédéric Hélein PDF

Trans. Amer. Math. Soc. 368 (2016), 6939-6978 Request permission

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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