The focusing energy-critical fourth-order Schrödinger equation with radial data
Benoît Pausader
In this paper, we investigate the focusing energy-critical fourth-order Schrödinger equation in the radial setting. We prove global existence and scattering for solutions of energy and $\dot{H}^2$-norm below that of the ground state.
keywords: nonlinear scattering. Fourth-order Schrödinger equation nonlinear dispersive equation focusing equation
Analyticity of the nonlinear scattering operator
Benoît Pausader Walter A. Strauss
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

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