报告题目： Long time asymptotic behavior of the short pulse equation: Riemann-Hilbert approach

报告人：徐建 副教授 （上海理工大学）

报告时间：2021年10月22日（周五）  09:00-11:30

报告地点：创新园大厦A1101

校内联系人：王振 教授  联系方式：84708351-8130

报告摘要： We mainly introduce the spectral analysis which is very different from the classical AKNS type Lax pair, such as NLS\MKdV equation, since the short pulse equation admits a WKI type negative order Lax pair. We show the solution of the initial value problem for the short pulse can be reconstructed in terms of the solution of a 2*2 matrix Riemann-Hilbert problem. Then, using the nonlinear steepest descent or Deift-Zhou method, we can obtain the leading order asymptotic behavior as time goes to infinity under no solitons assumption. And this result is more accurate than the result obtained by PDE method, because of the complete integrable property of the short pulse equation. We also show that the no solitons assumption is possible under some special initial value.

报告人简介：徐建，上海理工大学理学院副教授，博士毕业于复旦大学数学科学学院。主要从事可积系统和Riemann-Hilbert问题方面的研究。先后主持有国家和上海市自然科学基金青年项目和面上项目等多项研究课题。