Scattering Theory for Radial Nonlinear Schrödinger Equations on Hyperbolic Space
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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.
Keywords and phrases:Nonlinear Schrödinger equations on manifolds asymptotic behavior Strichartz estimates Morawetz estimates
AMS Mathematics Subject Classification:35B40 35P25 35Q55 58J37
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