For the 2D inhomogeneous NLS with 0<b<1 and α>2-b, radial H^1 solutions scatter in both focusing (below ground state) and defocusing cases.
A remark on the scattering theory for the 2d radial focusing INLS
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abstract
We consider the scattering results of the radial solutions below the ground state to the focusing inhomogeneous nonlinear Schr\"odinger equation $$i\partial_tu+\Delta u +|x|^{-b}|u|^{p}u=0$$ in two dimension, where $0<b<1$ and $2-b<p<\infty$. We use a modified version of Arora-Dodson-Murphy's approach [1] to give a new proof that extends the scattering results of [10] and avoids concentration compactness.
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2019 1verdicts
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Energy scattering for a class of inhomogeneous nonlinear Schr\"odinger equation in two dimensions
For the 2D inhomogeneous NLS with 0<b<1 and α>2-b, radial H^1 solutions scatter in both focusing (below ground state) and defocusing cases.