Analyticity of the scattering operator for semilinear dispersive equations

Abstract

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.

29 pages

References in corpus (6)

• Ill-posedness for nonlinear Schrodinger and wave equations
• Birkhoff Normal Form and Hamiltonian PDEs
• The cubic nonlinear Schrödinger equation in two dimensions with radial data
• Global well-posedness and scattering for the energy-critical nonlinear Schrödinger equation in R^3
• Global well-posedness and scattering for the defocusing energy-critical nonlinear Schrödinger equation in ${\mathbb{R}}^{1+4}$
• Semilinear Schrödinger Flows on Hyperbolic Spaces: Scattering in H^1