论文标题
长时间的渐近分析通过DBAR最陡峭的下降法进行非局部海洋方程
Long time asymptotic analysis for a nonlocal Hirota equation via the Dbar steepest descent method
论文作者
论文摘要
在本文中，我们主要关注具有加权Sobolev空间初始值的可集成非局部海洋方程的库奇问题。通过对LAX对的光谱分析，我们成功地将非局部Hirota方程的Cauchy问题转化为可解决的Riemann-Hilbert问题。此外，在没有离散光谱的情况下，通过DBAR最陡峭的下降方法获得了非局部Hirota方程溶液的长期渐近行为。不同于本地hirota方程，连续频谱上的领先顺序术语和$ q（x，t）$的剩余误差项受函数$imν（z_j）$的影响。
In this paper, we mainly focus on the Cauchy problem of an integrable nonlocal Hirota equation with initial value in weighted Sobolev space. Through the spectral analysis of Lax pairs, we successfully transform the Cauchy problem of the nonlocal Hirota equation into a solvable Riemann-Hilbert problem. Furthermore, in the absence of discrete spectrum, the long-time asymptotic behavior of the solution for the nonlocal Hirota equation is obtained through the Dbar steepest descent method. Different from the local Hirota equation, the leading order term on the continuous spectrum and residual error term of $q(x,t)$ are affected by the function $Imν(z_j)$.
