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Discrete and Continuous Dynamical Systems - Series A (DCDS-A)
 

Analyticity of the nonlinear scattering operator

Pages: 617 - 626, Volume 25, Issue 2, October 2009      doi:10.3934/dcds.2009.25.617

 
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BenoƮt Pausader - Department of Mathematics, Brown University, Providence, RI 02912, United States (email)
Walter A. Strauss - Department of Mathematics, Brown University, Providence, RI 02912, United States (email)

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.

Keywords:  Nonlinear scattering, nonlinear beam equation, NLKG, NLS, analytic operator.
Mathematics Subject Classification:  Primary: 74J25, 35P25; Secondary: 35Q72.

Received: March 2008;      Revised: April 2009;      Available Online: June 2009.