數(shù)學(xué)學(xué)術(shù)報告:From discrete integrable system to continuous integrable system
來源: 時間:2019-06-14
報告題目: From discrete integrable system to continuous integrable system 報 告 人: 馮寶峰教授(Baofeng Feng,University of Texas Rio Gande Valley) 報告時間:2019年6月19日(周三)10:00-11:00 報告地點:新波譜樓12樓1217報告廳
摘要:In this talk, I will give a review on recent development of integrable system, especially the discrete inegrable system. It is known that the tau-functions play a crucial role in both the continuous and discrete integrable sytems. We will start with a type of Gam determinant solution and show it satisfies the Hirota-Miwa equation, or the discrete Kadomtsev-Petviashvili (KP) equation. By introducing Schur polynomial, and Miwa transformation, we will derive the KP hierarchy, whose reductions give rise to the Korteweg-de Vries (KdV) equation and Boussinesq equation. Then we will show by simple transformations, the discrete KP equation can be transformed into discrete modified KP equation and the discrete KP-Toda lattice equation, which in turn lead to the modified KP and KP-Toda hierarchy, whose reductions give the modified KdV equation and Sine-Gordon equation, respectively.
講座預(yù)告
數(shù)學(xué)學(xué)術(shù)報告:From discrete integrable system to continuous integrable system
報告題目: From discrete integrable system to continuous integrable system
報 告 人: 馮寶峰教授(Baofeng Feng,University of Texas Rio Gande Valley)
報告時間:2019年6月19日(周三)10:00-11:00
報告地點:新波譜樓12樓1217報告廳
摘要:In this talk, I will give a review on recent development of integrable system, especially the discrete inegrable system. It is known that the tau-functions play a crucial role in both the continuous and discrete integrable sytems. We will start with a type of Gam determinant solution and show it satisfies the Hirota-Miwa equation, or the discrete Kadomtsev-Petviashvili (KP) equation. By introducing Schur polynomial, and Miwa transformation, we will derive the KP hierarchy, whose reductions give rise to the Korteweg-de Vries (KdV) equation and Boussinesq equation. Then we will show by simple transformations, the discrete KP equation can be transformed into discrete modified KP equation and the discrete KP-Toda lattice equation, which in turn lead to the modified KP and KP-Toda hierarchy, whose reductions give the modified KdV equation and Sine-Gordon equation, respectively.
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