Analyticity of the Scattering Operator for Semilinear Dispersive Equations
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چکیده
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 Schrödinger equation with powerlike 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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