Analyticity of the scattering operator for semilinear dispersive equations

Details Analyticity of the scattering operator for semilinear dispersive equations Analyticity of the scattering operator for semilinear dispersive equations

2008-01-24

arxiv.org/abs/0801.3774v1

Communications in Mathematical Physics 286, 3 (2009) 1181-1209

Mathematics

Analysis of PDEs

29 pages

Scientific paper

10.1007/s00220-008-0599-x

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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