报告题目：The Long-time asymptotics of some soliton equations
报 告 人：耿献国（郑州大学 教授）
报告时间：2022年12月6日 下午3:30开始
报告地点：腾讯会议（会议号：156 899 705）
报告摘要：Based on the matrix block technique, the Deift-Zhou nonlinear steepest descent method is developed to study the asymptotic analysis of solutions of some nonlinear evolution equations associated with the higher-order matrix spectral problems. As applications, spectral analysis of the 4×4 matrix spectral problems related to these soliton equations is discussed and and their scattering data are obtained, from which the solutions to the Cauchy problems of these soliton equations are transformed into the solutions to the corresponding Riemann–Hilbert problems. The Deift–Zhou nonlinear steepest descent method is extended to these Riemann–Hilbert problems, and model Riemann–Hilbert problems are established with the help of distinct factorizations of the jump matrixs for the Riemann–Hilbert problems. Finally, the long-time asymptotics of the solutions to the Cauchy problems of these soliton equations are obtained.
报告人简介：耿献国，郑州大学博彩导航
教授，博士生导师，郑州大学特聘教授。国务院政府特殊津贴专家，全国百篇优秀博士学位论文指导老师。从事的研究方向是可积系统及应用。曾在Commun. Math. Phys., Trans. Amer. Math. Soc., Adv. Math., J. Nonlinear Sci., SIAM J. Math. Anal.等刊物上发表论文。主持国家自然科学基金重点项目2项和多项国家自然科学基金面上项目等。
