论文标题
长时间渐近分析用于散焦Ablowitz-ladik系统，初始值较低。
Long-time asymptotic analysis for defocusing Ablowitz-Ladik system with initial value in lower regularity
论文作者
论文摘要
最近，通过反光谱方法，我们为在离散的sobolev space $ l^{2,1} $中脱落Ablowitz-ladik系统的$ l^2 $ bijectitive。基于这些结果，本文的目的是研究散落的Ablowitz-Ladik系统的初始评估问题的长期渐近特性，其初始潜力较低。主要思想是用单位圆对核心riemann-hilbert问题进行适当的变形和分析，作为跳跃轮廓$σ$。结果，我们表明，当$ | \ frac {n} {2t} | \ le 1 <1 $时，该解决方案允许Zakharov-Manakov类型公式，当$ | \ frac {n} {2t} {2t} | \ ge 1> 1 $时，该解决方案降至零。
Recently, we have given the $l^2$ bijectivity for defocusing Ablowitz-Ladik systems in the discrete Sobolev space $l^{2,1}$ by inverse spectral method. Based on these results, the goal of this article is to investigate the long-time asymptotic property for the initial-valued problem of the defocusing Ablowitz-Ladik system with initial potential in lower regularity. The main idea is to perform proper deformations and analysis to the corespondent Riemann-Hilbert problem with the unit circle as the jump contour $Σ$. As a result, we show that when $|\frac{n}{2t}|\le 1<1$, the solution admits Zakharov-Manakov type formula, and when $|\frac{n}{2t}|\ge 1>1$, the solution decays fast to zero.
