Analyticity of the nonlinear scattering operator

Benoît Pausader; Walter A. Strauss

doi:10.3934/dcds.2009.25.617

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2009, Volume 25, Issue 2: 617-626. Doi: 10.3934/dcds.2009.25.617

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Analyticity of the nonlinear scattering operator

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

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

Received: February 29, 2008

Revised: March 31, 2009

Published: May 2009

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Abstract

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.

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Mathematics Subject Classification: Primary: 74J25, 35P25; Secondary: 35Q72.

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