In this talk, we report our recent work on the asymptotic analysis of the focusing NLS equation and focusing KE equation by the nonlinear steepest descent method of Deift and Zhou. The first part introduces the long-time asymptotic behaviors of two separable plane waves of the focusing NLS equation. The second part focuses on the far-field behaviors of multiple-pole solitons of the focusing NLS equation in the large-order limit. Finally, the long-time asymptotics of the focusing KE equation with nonzero boundary conditions at infinity is reported briefly.

王灯山，北京师范大学数学科学学院，教授、博士生导师。主要从事可积系统和渐近分析方面的研究，主持国家自然科学基金面上项目等国家级和省部级项目10余项，参与获得北京市科学技术奖一等奖。入选北京市“科技新星”计划、北京市“高创计划”青年拔尖人才和北京市“长城学者”计划。