报告时间：2025年10月10日 下午16:00开始
报 告 人：Jianke Yang (杨建科) 教授，The University of Vermont
报告地点：9-113
报告题目：Wave Patterns in Higher-Order KP-I Lumps
报告摘要: The Kadomtsev-Petviashvili-I (KP-I) equation models two-dimensional shallow water waves under strong surface tension as well as the evolution of weakly nonlinear two-dimensional plasma waves. In this talk, pattern formation in higher-order lumps of the KP-I equation at large times is analytically studied. For these higher-order lumps under certain internal-parameter restrictions, we show that the large-time wave patterns comprise fundamental lumps arranged in non-triangular shapes in the outer region, which are described analytically by nonzero-root structures of the Wronskian-Hermit polynomials, together with fundamental lumps arranged in triangular shapes in the inner region, which are described analytically by root structures of the Yablonskii-Vorob'ev polynomials. When time evolves from large negative to large positive, the non-triangular pattern in the outer region switches its x and y directions, while the triangular pattern in the inner region reverses its direction along the x-axis. For higher-order lumps under generic internal-parameter values, however, we show that the large-time patterns would comprise fundamental lumps in the outer region that are described analytically by the nonzero-root structures of the Wronskian–Hermite polynomials, together with fundamental lumps in the inner region that are uniformly distributed on concentric rings. Our predicted patterns at large times are compared to true solutions, and excellent agreement is observed.
报告人简介：杨建科，佛蒙特大学威廉姆斯数学教授、校聘杰出教授、美国光学学会会士。1994年在MIT获得博士学位，主要研究领域聚焦于非线性波及其物理应用。长期从事非线性光学的物理和数学理论的前沿研究，并做出了一系列有国际影响力的工作，在Phys. Rev. Lett, J. Comput. Phys., J. Nonlinear Sci., Physica D, SIAM J. Appl. Math, Stud. Appl. Math 等国际重要期刊上发表论文百余篇，出版专著多部。