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- W4282831886 abstract "We investigate the well-posedness theory of the 2-D fractional nonlinear Schrödinger equation (NLSE) with a mixed degree of derivatives. Motivated by models in optics and photonics where the light propagation is governed by non-quadratic, fractional, and anisotropic dispersion profile, this paper presents first results in this direction. Dispersive estimates are developed in the context of anisotropic Sobolev spaces defined by inhomogeneous symbols. The main model is shown to exhibit scattering for small data in the scaling-critical space. Furthermore the continuity of solution with respect to the dispersion parameter is shown on a compact time interval." @default.
- W4282831886 created "2022-06-15" @default.
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- W4282831886 date "2022-12-01" @default.
- W4282831886 modified "2023-10-17" @default.
- W4282831886 title "Well-posedness of the mixed-fractional nonlinear Schrödinger equation on <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML display=inline id=d1e22 altimg=si1.svg><mml:msup><mml:mrow><mml:mi mathvariant=double-struck>R</mml:mi></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msup></mml:math>" @default.
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- W4282831886 doi "https://doi.org/10.1016/j.padiff.2022.100406" @default.
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