报告题目：An effective description of high-frequency non-polarized wave-packet propagation

报告人：孟鑫 东北师范大学

报告时间：2025年11月16日 下午14:00-15:00

报告地点：#腾讯会议：544-638-730

校内联系人 张剑桥 [email protected]

报告摘要：In this talk, we consider semilinear hyperbolic systems with a small perturbation parameter. We are interested in an effective description of high-frequency wave-packet propagation associated to highly oscillatory initial conditions. For polarized initial conditions, classical perturbation analysis yields NLS approximations up to an arbitrary order. For non-polarized initial conditions, in lowest order a system of decoupled NLS equations can be derived as an approximate description of the associated solutions. Assuming non-resonance conditions, we prove estimates that rigorously control the error between these formal approximations and true solutions of the original system. The estimates imply that solutions to non-polarized initial conditions split into polarized wave-packets. The interaction of these wave packets results in phase and envelope shifts, for which explicit formulas are provided.

报告人简介：2020年于吉林大学获得学士学位，2025年于吉林大学获得博士学位，目前为东北师范大学数学与统计学院博士后。主要研究方向为微分方程与动力系统。