nls -塞格格方程的长时间行为

IF 1.1 3区数学 Q2 MATHEMATICS, APPLIED

Dynamics of Partial Differential Equations Pub Date : 2019-01-01 DOI:10.4310/dpde.2019.v16.n4.a2

Ruoci Sun

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引用次数: 3

摘要

．我们感兴趣的是正傅立叶模滤波对可积非线性薛定谔方程的影响。同样地，我们想研究色散对三次Szeg“o”方程的影响，从而得到NLS-Szeg“o”方程对圆s1的影响。第一个结果与Sobolev对小数据的长时间估计有关。第二组结果涉及平面波解的轨道稳定性。也得到了一些不稳定的结果，导致波浪湍流现象。

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Long time behavior of the NLS-Szegő equation

. We are interested in the inﬂuence of ﬁltering the positive Fourier modes to the integrable non linear Schr¨odinger 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 S 1 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.

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来源期刊

Dynamics of Partial Differential Equations 数学-应用数学

CiteScore

2.00

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： Publishes novel results in the areas of partial differential equations and dynamical systems in general, with priority given to dynamical system theory or dynamical aspects of partial differential equations.