论文标题
$ \ dbar $ - 振动性riemann-hilbert问题的最终下降方法
A $\dbar$-steepest descent method for oscillatory Riemann-Hilbert problems
论文作者
论文摘要
我们研究了在可集成方程的AKNS层次结构中产生的Riemann-Hilbert问题（RHP）的渐近行为。我们的分析基于$ \ dbar $ steepest下降方法。我们考虑由$ h^{1,1}（\ r）$初始数据的AKNS层次结构的反散射变换产生的RHP。该分析将分为三个区域：快速衰减区域，振荡区域和自相似区域（Painlevé地区）。所得公式可以直接应用于研究NLS，MKDV等可集成方程的溶液的长期渐近差异及其高阶概括。
We study the asymptotic behavior of Riemann-Hilbert problems (RHP) arising in the AKNS hierarchy of integrable equations. Our analysis is based on the $\dbar$-steepest descent method. We consider RHPs arising from the inverse scattering transform of the AKNS hierarchy with $H^{1,1}(\R)$ initial data. The analysis will be divided into three regions: fast decay region, oscillating region and self-similarity region (the Painlevé region). The resulting formulas can be directly applied to study the long-time asymptotic of the solutions of integrable equations such as NLS, mKdV and their higher-order generalizations.
