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 (7)

• Ill-posedness for nonlinear Schrodinger and wave equations
• Birkhoff Normal Form and Hamiltonian PDEs
• The nonlinear Schrödinger equation with combined power-type nonlinearities
• 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

Cited by in corpus (9)

• Inverse Scattering for Critical Semilinear Wave Equations
• A nonlinear Landau-Zener formula
• On nonlinear scattering for quantum walks
• Breakdown of regularity of scattering for mass-subcritical NLS
• Deconvolutional determination of the nonlinearity in a semilinear wave equation
• Scattering and inverse scattering for nonlinear quantum walks
• On recovering the nonlinearity for generalized higher-order Schrödinger equations
• Dynamics near the origin of the long range scattering for the one-dimensional Schrodinger equation
• Analyticity and infinite breakdown of regularity in mass-subcritical Hartree scattering