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甬江数学讲坛174讲(2021年第33讲)
2021-06-16 10:39     (点击:)

报告题目:Universal rogue wave patterns

  人:杨建科(佛蒙特大学 教授)

报告时间:2021617 上午9:00开始

报告地点Zoom会议链接:https://zoom.us/j/7323017223?pwd=RisyVGJteUU3eU50ZlZvdFd1NTZrUT09

                    ID: 732 301 7223   Passcode: nbu2021

报告摘要:We 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. This talk is based on joint work with Dr. Bo Yang.

报告人简介:杨建科,佛蒙特大学教授,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。

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