First integrals for nonlinear dispersive equations

Frédéric Hélein (1)

1 IMJ-PRG (UMR_7586) - Institut de Mathématiques de Jussieu - Paris Rive Gauche

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 this theory is based on a new suitable formulation of the dynamics of solutions of dispersive equations.

Mots clés: Dispersive Partial Differential Equations; Nonlinear Wave Equations; Nonlinear Klein-Gordon Equation; Schrodinger Equation; Mathematical Physics; General Relativity

Domaines: Equations aux dérivées partielles [math.AP]

Frédéric Hélein. First integrals for nonlinear dispersive equations. 2013. ⟨hal-00879582⟩