Energy scattering for a class of the defocusing inhomogeneous nonlinear Schrödinger equation

Scattering for the Radial Focusing Inhomogeneous NLS Equation in Higher Dimensions

“…This new approach will be very important to carry out the analysis in the present study. For other recent works about the INLS model we refer the reader to Hong (2016), Killip et al (2017), Lu et al (2018), Combet and Genoud (2016), Dinh (2018Dinh ( , 2019.…”

Scattering in the weighted <inline-formula><tex-math id="M1">\begin{document}$ L^2 $\end{document}</tex-math></inline-formula>-space for a 2D nonlinear Schrödinger equation with inhomogeneous exponential nonlinearity

“…This is why we restrict ourselves to initial data belonging to the weighted L 2 -space Σ := H 1 ∩ L 2 (|x| 2 dx). Note that the scattering in Σ for the NLS with N (x, u) = |x| −b |u| α u was considered by the second author in [10].…”

The Sobolev-Morawetz approach for the energy scattering of nonlinear Schrödinger-type equations with radial data

“…More precisely, we have the following result. and 10) where σ c := 1−γc γc = γ+2−(N −2)(p−1) N (p−1)−γ−2 . Then the corresponding solution to (NLC) exists globally in time and scatters in H 1 in both directions.…”

“…He also extended the validity of b in dimensions N ≥ 3. Recently, Xu-Zhao [41] and the first author in [10] has simultaneously proved the energy scattering for (5.2) in the two dimensions. where F and F −1 are the Fourier transform and inverse Fourier transform respectively.…”