报告题目：Painleve transcendents in the defocusing mKdV equation with non-zero boundary conditions

报 告 人：范恩贵 教授

报告时间：2025年10月20日（星期一）上午10:45

报告地点：上海理工大学卓越楼，810会议室

报告摘要：We consider the Cauchy problem for the defocusing modified Korteweg-de Vries (mKdV) equation with non-zero boundary conditions, which can be characterized by a Riemann-Hilbert problem through the inverse scattering transform. Using the dbar-generalization of the Deift-Zhou nonlinear steepest descent approach, combined with a double scaling limit technique, we obtain the long-time asymptotics of the solution of the Cauchy problem for the defocusing mKdV equation in the transition region. The asymptotics can be expressed in terms of the solution of the second  Painleve transcendent.

报告人简介:范恩贵，复旦大学数学科学学院教授、博士生导师。主要研究方向是孤立子理论、Riemann-Hilbert问题、正交多项式和随机矩阵理论。主持国家自然科学基金、上海曙光计划等多项研究课题。在《Communications in Mathematical Physics》、《Advance in Mathematics 》、 《SIAM Journal of  Mathematical Analysis》、《Journal Differential Equations》等国际重要期刊发表论文100余篇，被SCI刊源他引3000余次。获教育部自然科学二等奖、上海市自然科学二等奖、复旦大学谷超豪数学奖等荣誉。