Well-posedness of the mixed-fractional nonlinear Schrödinger equation on R2
Well-posedness of the mixed-fractional nonlinear Schrödinger equation on R2
复制标题
R2 上混合分数阶非线性薛定谔方程的适定性
DOI：
10.1016/j.padiff.2022.100406
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发表时间：
2022
影响因子：
--
通讯作者：
Aceves, Alejandro
中科院分区：
文献类型：
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作者：
Choi, Brian;Aceves, Alejandro
研究了具有混合阶导数的2-D分数阶非线性薛定谔方程的适定性理论。在光学和光子学模型的启发下，光的传播是由非二次，分数，和各向异性的色散曲线，本文提出了在这个方向上的第一个结果。色散估计的上下文中的各向异性Sobolev空间定义的非齐次符号。主模型显示出分散的小数据在缩放临界空间。进一步证明了解关于色散参数的连续性。
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.