阶跃初值Korteweg-de Vries方程的参数化问题
Parametrix problem for the Korteweg--de Vries equation with steplike initial data
摘要：
本文研究了具有阶跃初值的Korteweg--de Vries方程解的渐近性，它导致激波在渐近常数区和孤子区之间的区域，即$t \rightarrow \infty$。为了实现这一点，我们提出了一种替代方法，通常的参数涉及一个小的范数黎曼-希尔伯特问题，这是基于直接比较的解决方案，而相应的黎曼-希尔伯特问题。这种方法的动机源于这样一个事实，即我们的问题的可逆全纯全局参数解不存在某些离散时间。
英文摘要：
In this paper we study the asymptotics of solutions to the Korteweg--de Vries equation with steplike initial data, which lead to shock waves in the region between the asymptotically constant region and the soliton region, as $t \rightarrow \infty$. To achieve this, we present an alternative approach to the usual argument involving a small norm Riemann--Hilbert problem, which is based instead on the direct comparison of resolvents related to the corresponding Riemann--Hilbert problems. The motivation for this approach stems from the fact that an invertible holomorphic global parametrix solution for our problem does not exist for certain discrete times.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
