论文标题
在一个空间维度中的立方非线性schrödinger方程系统的多项式减速
Polynomial deceleration for a system of cubic nonlinear Schrödinger equations in one space dimension
论文作者
论文摘要
在本文中，我们考虑了立方非线性schrödinger方程的特定系统的初始值问题。这项研究的目的是指定$ l^{\ infty} $中解决方案的渐近配置文件为$ t \ to \ infty $。然后发现，溶液衰减比线性溶液慢。此外，衰减率的差异是多项式阶。衰减的这种减速是由于非线性的扩增效应。这种非线性扩增现象以前以几种特定系统而闻名，但是这些结果中衰减的减速是通过对数顺序的。据我们所知，本文研究的系统是第一个模型，因为以多项式顺序减速是合理的。
In this paper, we consider the initial value problem of a specific system of cubic nonlinear Schrödinger equations. Our aim of this research is to specify the asymptotic profile of the solution in $L^{\infty}$ as $t \to \infty$. It is then revealed that the solution decays slower than a linear solution does. Further, the difference of the decay rate is a polynomial order. This deceleration of the decay is due to an amplification effect by the nonlinearity. This nonlinear amplification phenomena was previously known for several specific systems, however the deceleration of the decay in these results was by a logarithmic order. As far as we know, the system studied in this paper is the first model in that the deceleration in a polynomial order is justified.
