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数学学科动力系统与非线性分析研究所学术报告(杨建科 美国佛蒙特大学)

发布者:戴 情   发布时间:2021-06-29  浏览次数:146

TitleUniversal rogue wave patterns associated with the Yablonskii-Vorob’ev polynomial hierarchy 

报告人杨建科   美国佛蒙特大学教授

报告时间72日周五上午9:00-10:00

报告地点:腾讯会议    https://meeting.tencent.com/s/7JDZt9WYgYMr

                    ID:914 540 992

AbstractWe show that universal rogue wave patterns exist in integrable systems. These rogue patterns comprise fundamental rogue waves arranged in shapes such as a triangle, pentagon and heptagon, with a possible lower-order rogue wave at the center. These patterns appear when one of the internal parameters in bilinear expressions of rogue waves gets large. Analytically, these patterns are determined by the root structures of the Yablonskii-Vorob’ev polynomial hierarchy through a linear transformation. Thus, the induced rogue patterns in the space-time plane are simply the root structures of Yablonskii-Vorob’ev hierarchy polynomials under actions such as dilation, rotation, stretch, shear and translation. Which level of the Yablonskii-Vorob’ev hierarchy is determined by which internal parameter is chosen to be large, and which polynomial at that level of the hierarchy is determined by the order of the underlying rogue wave. As examples, these universal rogue patterns are explicitly determined and graphically illustrated for the nonlinear Schrodinger equation, the derivative nonlinear Schrodinger equation, the Boussinesq equation, and the Manakov system.


简介:杨建科,美国佛蒙特大学数学与统计系教授,博士生导师。1994年在MIT获得博士学位,长期从事非线性光学的物理和数学理论的前沿研究,并做出了一系列有国际影响力的工作。出版专著一部,并在 Stud. Appl. Math.  Phys. DJ. Nonlinear Sci.SIAM J. Appl. Math. J. Comput. Phys.Phys. Rev. E 等国际重要期刊上发表论文80余篇。


邀请人:动力系统研究团队

 

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