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2022.6.15,冯宝峰 教授,美国 The University of Texas Rio Grande Valley,Ocean waves, soliton-like movement of rigid pendula and discrete Kadomtsev-Petviashvili (KP) equation

报告题目:Ocean waves, soliton-like movement of rigid pendula and discrete Kadomtsev-Petviashvili (KP) equation

报告人:冯宝峰 教授 美国 The University of Texas Rio Grande Valley

报告摘要:In this talk, we are going to connect two different physical phenomena: ocean waves usually observed on the beach and the soliton-like movement of rigid pendula attached to a stretched wire with an integrable discrete equation in three-dimensional lattice space, the so-called discrete Kadomtsev-Petviashvili (KP) equation. First, we show the videos of these two interesting phenomena and present the mathematical models behind them. Then, we turn to a totally different object, i.e., discrete KP equation, discussing its connection with two theorems in geometry: Menelaus Theorem and Desargues Theorem, its Lax pair and determinant solutions. Amazingly, we show that the discrete KP equation can generate mathematical models of above two physical phenomena along with their solutions. If time permits, we will continue to show that a geometry object, the so-called reciprocal triangles discovered by Maxwell in 1864, can generate a discrete KP equation of B type, from which we can generate many other mathematical models such as the Sawada-Kotera equation and coupled Ablowitz-Ladik lattice equation.


时间:2022615日(星期三)上午9:00 --- 11:00


腾讯会议:359-735-110