报告题目：The Degasperis-Procesi equation on the line: Soliton resolution, asymptotic stability of N-solitons, Painlevé and Airy asymptotics

报告人：范恩贵教授

摘要：The Degasperis-Procesi (DP) equation as a model to describe the propagation of shallow water waves, is a completely integrable system and admits a 3*3 matrix Lax pair. In this paper, for the Cauchy problem of the DP equation for generic initial data in Schwarz space that can support solitons, we give a full description of the long-time asymptotics for the DP equation in the whole upper half-plane. Using the D-bar generalization of the Deift-Zhou nonlinear steepest descent method and a double limit technique, we derive the leading order approximation to the solution u(x, t) of the DP equation for large times in the following three types of space-time regions.

报告人简介：范恩贵，复旦大学教授、博士生导师、上海市曙光学者,主要研究方向：可积系统和反散射理论；主持国家自然科学基金、上海曙光计划等多项研究课题。在Adv. Math.、Comm. Math. Phys.、SIAM J. Math. Anal.、J. Differential Equations等国际重要期刊发表论文150余篇。应邀访问美国密苏里大学、密西根州立大学、德克萨斯大学、日本京都大学、香港大学等。曾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。

时间：2024年3月23日（星期六），10:00-11:00

地点：数学楼2-1会议室