Global well-posedness for the cubic nonlinear Schrödinger equation with initial data lying in <i>L</i><sup><i>p</i></sup>-based Sobolev spaces
نویسندگان
چکیده
In this paper we continue our study [DSS20] of the nonlinear Schr\"odinger equation (NLS) with bounded initial data which do not vanish at infinity. Local well-posedness on $\mathbb{R}$ was proved for real analytic data. Here prove global 1D NLS lying in $L^{p}$ any $2 < p \infty$, provided is sufficiently smooth. We use complete integrability cubic Schr{\"o}dinger equation.
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ژورنال
عنوان ژورنال: Journal of Mathematical Physics
سال: 2021
ISSN: ['0022-2488', '1527-2427', '1089-7658']
DOI: https://doi.org/10.1063/5.0042321