Scattering Theory for Radial Nonlinear Schrödinger Equations on Hyperbolic Space
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- Banica, V., Carles, R. & Staffilani, G. GAFA Geom. funct. anal. (2008) 18: 367. doi:10.1007/s00039-008-0663-x
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We study the long-time behavior of radial solutions to nonlinear Schrödinger equations on hyperbolic space. We show that the usual distinction between short-range and long-range nonlinearity is modified: the geometry of the hyperbolic space makes every power-like nonlinearity short range. The proofs rely on weighted Strichartz estimates, which imply Strichartz estimates for a broader family of admissible pairs, and on Morawetz-type inequalities. The latter are established without symmetry assumptions.