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arXiv · 2401.10939

Profile decomposition and scattering for general nonlinear Schr{\"o}dinger equations

Thomas Duyckaerts·Phan van Tin
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Abstract

We consider a Schr{\"o}dinger equation with a nonlinearity which is a general perturbation of a power'' nonlinearity. We construct a profile decomposition adapted to this nonlinearity.We also prove global existence and scattering in a general defocusing setting, assuming thatthe critical Sobolev norm is bounded in the energy-supercritical case. This generalizes severalprevious works on double-power nonlinearities.

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Thomas Duyckaerts, Phan van Tin. 2024-01-17. Profile decomposition and scattering for general nonlinear Schr{\"o}dinger equations. https://arxiv.org/abs/2401.10939

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