Analyticity of the nonlinear scattering operator

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July 2009, 25(2): 617-626. doi: 10.3934/dcds.2009.25.617

Analyticity of the nonlinear scattering operator

Benoît Pausader ^1, and Walter A. Strauss ^1,

1.	Department of Mathematics, Brown University, Providence, RI 02912, United States, United States

Received March 2008 Revised April 2009 Published June 2009

Abstract
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We present a new and simpler proof that the nonlinear scattering operator $\S$ is analytic on energy space. We apply it in particular to a fourth-order nonlinear wave equation in Rⁿ. In addition, we prove that $\S$ determines the scatterer uniquely and that for small powers there is no scattering.

Keywords: NLS, nonlinear beam equation, analytic operator., Nonlinear scattering, NLKG.

Mathematics Subject Classification: Primary: 74J25, 35P25; Secondary: 35Q7.

Citation: Benoît Pausader, Walter A. Strauss. Analyticity of the nonlinear scattering operator. Discrete & Continuous Dynamical Systems - A, 2009, 25 (2) : 617-626. doi: 10.3934/dcds.2009.25.617

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