报告人：周汝光 教授 江苏师范大学

报告题目：Algebro-geometric solutions of the Ablowitz-Kaup-Newell-Segur system with space-inverse reductions

时间：2025年5月24日15:00-16:00

地点：数学楼2-1会议室

摘要：

We investigate algebro-geometric solutions of the Ablowitz-Kaup-Newell-Segur (AKNS) system under space-inverse reductions. By extending the method of nonlinearizations of the Lax pair to the AKNS equation with these reductions, we derive a new class of finite-dimensional Hamiltonian systems. These systems are nonlocal due to their dependence on the inverse of the space variable. We prove that these nonlocal Hamiltonian systems remain Liouville integrable and can be linearized on the Jacobi variety. Furthermore, we demonstrate how to construct algebro-geometric solutions of the AKNS equation with space-inverse reductions using these nonlocal Hamiltonian systems. As applications, we obtain algebro-geometric solutions for the AKNS equation with Dirichlet and Neumann boundary conditions, as well as for the nonlocal nonlinear Schrödinger (NLS) equation

报告人简介：

周汝光，江苏师范大学数学与统计学院教授，曾担任江苏师范大学校长。1997年在复旦大学获基础数学方向理学博士。长期从事可积系统的数学理论研究，博士论文获2000年全国优秀博士论文，2001-2002年在德国Paderborn大学任Humboldt学者。研究成果获教育部自然科学二等奖。

邀请人：刘小川 教授