学术报告
报告题目：Infinite order rogue waves
报告人：凌黎明，教授、博士生导师
报告时间：2020年12月12日14:00-15:30
腾讯会议：会议 ID：812 221 132
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报告摘要：In this talk, we would like to introduce the fundamental rogue wave solutions of the focusing nonlinear Schrödinger equation in the limit of large order. Using the robust inverse scattering method, we establish the existence of a limiting profile of the rogue wave in the large-k limit when the solution is viewed in appropriate rescaled variables capturing the near-field region where the solution has the largest amplitude. The limiting profile is a new particular solution of the focusing nonlinear Schrödinger equation in the rescaled variables—the rogue wave of infinite order—which also satisfies ordinary differential equations with respect to space and time. The spatial differential equations are identified with certain members of the Painlevé-III hierarchy. We analyze the far-field asymptotic behavior of the near-field limit solution and compare the asymptotic formulas with the exact solution using numerical methods for solving Riemann–Hilbert problems. In a certain transitional region for the asymptotics, the near-field limit function is described by a specific globally defined tritronquée solution of the Painlevé-II equation. These properties lead us to regard the rogue wave of infinite order as a new special function. (This work is jointed with Deniz and Peter)
专家简介：报告人长期从事非线性可积系统的研究，在可积系统“怪波”理论的发展中作出了一系列工作，同合作者给出高阶怪波解的Darboux 变换方法以及无穷阶怪波的分析理论。 报告人在该方向上已经发表 40余篇 SCI 论文，其中 Duke Mathematical Journal， Physical Review E，Physica D, Nonlinearity 等杂志，合作出版怪波专著一部。 已发表文章在 Google 学术搜索统计引用 2000 余次，H 指数 16，其中单篇最高引用 500 次，4篇入选ESI高被引论文。曾主持国家自然科学基金项目2项。