Asymptotic behavior in time of solution to system of cubic nonlinear Schr"odinger equations in one space dimension
Asymptotic behavior in time of solution to system of cubic nonlinear Schr"odinger equations in one space dimension
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发表时间：
2021-12
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通讯作者：
Satoshi Masaki;J. Segata;Kota Uriya
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作者：
Satoshi Masaki;J. Segata;Kota Uriya
本文考虑一维空间中两个三次非线性薛定谔方程组解的大时间渐近性态。结果表明，对于一个系统，存在一个小解，它的渐近轮廓是以不同方式振荡的两个部分的和。这种行为似乎是新的。在此基础上，给出了几个具有修正散射、非线性放大和非线性耗散等行为的系统的例子。我们还推广了以前的非线性三次系统的分类结果。
In this paper, we consider the large time asymptotic behavior of solutions to systems of two cubic nonlinear Schrödinger equations in one space dimension. It turns out that for a system there exists a small solution of which asymptotic profile is a sum of two parts oscillating in a different way. This kind of behavior seems new. Further, several examples of systems which admit solution with several types of behavior such as modified scattering, nonlinear amplification, and nonlinear dissipation, are given. We also extend our previous classification result of nonlinear cubic systems.