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- W2937226765 abstract "We are interested in the influence of filtering the positive Fourier modes to the integrable non linear Schr{o}dinger equation. Equivalently, we want to study the effect of dispersion added to the cubic Szeg{o} equation, leading to the NLS-Szeg{o} equation on the circle $mathbb{S}^1$begin{equation*}i partial_t u + epsilon^{alpha}partial_x^2 u = Pi(|u|^2 u),qquad 0<epsilon<1, qquad alphageq 0.end{equation*}There are two sets of results in this paper. The first result concerns the long time Sobolev estimates for small data. The second set of results concerns the orbital stability of plane wave solutions. Some instability results are also obtained, leading to the wave turbulence phenomenon." @default.
- W2937226765 created "2019-04-25" @default.
- W2937226765 creator A5089793467 @default.
- W2937226765 date "2019-04-19" @default.
- W2937226765 modified "2023-10-18" @default.
- W2937226765 title "Long time behavior of the NLS-Szeg{o} equation" @default.
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- W2937226765 doi "https://doi.org/10.48550/arxiv.1904.09182" @default.
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