We prove H1 scattering for a defocusing NLS on the line with fully variable coefficients. The result is proved by adapting the Kenig–Merle scheme to a non-translation invariant setting. In addition, we give an abstract version of the scheme which can be applied to other operators. We also consider the focusing case, and we prove scattering for a suitable subset of initial data.
Scattering for the NLS on the line with variable coefficients / D'Ancona, Piero; Zanni, Angelo. - In: COMMUNICATIONS ON PURE AND APPLIED ANALYSIS. - ISSN 1534-0392. - 25:0(2026), pp. 214-245. [10.3934/cpaa.2025096]
Scattering for the NLS on the line with variable coefficients
D'Ancona, Piero
;Zanni, Angelo
2026
Abstract
We prove H1 scattering for a defocusing NLS on the line with fully variable coefficients. The result is proved by adapting the Kenig–Merle scheme to a non-translation invariant setting. In addition, we give an abstract version of the scheme which can be applied to other operators. We also consider the focusing case, and we prove scattering for a suitable subset of initial data.File allegati a questo prodotto
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