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On scattering for the quintic defocusing nonlinear Schrödinger equation on R×T2
 Comm. Pure and Appl. Math
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Modified scattering for the cubic Schrödinger equation on product spaces and applications
, 2013
"... Abstract. We consider the cubic nonlinear Schrödinger equation posed on the spatial domain R × Td. We prove modified scattering and construct modified wave operators for small initial and final data respectively (1 ≤ d ≤ 4). The key novelty comes from the fact that the modified asymptotic dynamics ..."
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Cited by 7 (3 self)
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Abstract. We consider the cubic nonlinear Schrödinger equation posed on the spatial domain R × Td. We prove modified scattering and construct modified wave operators for small initial and final data respectively (1 ≤ d ≤ 4). The key novelty comes from the fact that the modified asymptotic dynamics are dictated by the resonant system of this equation, which sustains interesting dynamics when d ≥ 2. As a consequence, we obtain global strong solutions (for d ≥ 2) with infinitely growing high Sobolev norms Hs. 1.
Conditional global existence and scattering for a semilinear Skyrme equation with large data
, 2013
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Global existence, scattering and blowup for the focusing NLS on the hyperbolic space
, 2014
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PROFILE DECOMPOSITIONS FOR WAVE EQUATIONS ON HYPERBOLIC SPACE WITH APPLICATIONS
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"... Abstract In this paper we show the existence of radial positive stationary solutions to the energy critical nonlinear Schrödinger equation on H 3 by reducing the problem to an ODE. We also make an observation that KenigMerle's variational argument in [2] can work even without the existence of ..."
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Abstract In this paper we show the existence of radial positive stationary solutions to the energy critical nonlinear Schrödinger equation on H 3 by reducing the problem to an ODE. We also make an observation that KenigMerle's variational argument in [2] can work even without the existence of a positive stationary solution, based on this, we sketch a possible strategy which may recover their result in [2] on H 3 .
4 STABILITY OF STATIONARY EQUIVARIANT WAVE MAPS FROM THE HYPERBOLIC PLANE
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