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Article Dans Une Revue Communications in Mathematical Physics Année : 2009

Analyticity of the scattering operator for semilinear dispersive equations

Résumé

We present a general algorithm to show that a scattering operator associated to a semilinear dispersive equation is real analytic, and to compute the coefficients of its Taylor series at any point. We illustrate this method in the case of the Schrodinger equation with power-like nonlinearity or with Hartree type nonlinearity, and in the case of the wave and Klein-Gordon equations with power nonlinearity. Finally, we discuss the link of this approach with inverse scattering, and with complete integrability.
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Dates et versions

hal-00216145 , version 1 (24-01-2008)

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Rémi Carles, Isabelle Gallagher. Analyticity of the scattering operator for semilinear dispersive equations. Communications in Mathematical Physics, 2009, 286 (3), pp.1181-1209. ⟨10.1007/s00220-008-0599-x⟩. ⟨hal-00216145⟩
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