短脉冲方程的长时间渐近分析

活动信息

  • 开始时间:2021-10-22 09:00
  • 活动地点:创新园大厦A1101
  • 主讲人:徐建

活动简介

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 reconstructd 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.

主讲人介绍

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
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