講演会

 

English Version

 

 

 

11

日時:2017年7月11日火曜日 午後5時15分 − 午後6時45分

場所:早稲田大学西早稲田キャンパス62W号館大会議室

 

題目:On nonlocal nonlinear Schrodinger equation and its discrete version

 

講演者:Prof. Zuo-Nong Zhu,   Shanghai Jiao Tong University,  P. R. China

概要: Very recently, Ablowitz and Musslimani introduced reverse space, reverse time, and reverse space-time nonlocal nonlinear integrable equations including the reverse space nonlocal NLS equation, the real and complex reverse space-time nonlocal mKdV, sine-Gordon, Davey-Stewartson equations, et.al. In this talk, we will show that, under the gauge transformations, the nonlocal focusing NLS (and it discrete version) and the nonlocal defocusing NLS (and it discrete version) are, respectively, gauge equivalent to the coupled Heisenberg equation (and it discrete version) and the coupled modified Heisenberg equation (and it discrete version). We will discuss the construction of discrete soliton solutions for the discrete nonlocal focusing NLS. We will demonstrate that the discrete soliton yields soliton of nonlocal focusing NLS under the continuous limit. The relations of these solutions between nonlocal NLS and classical NLS will be given. This is a joint work with Dr. Li-yuan Ma.

 

10

日時:2017年6月10日土曜日 午後1時 − 午後4時

場所:早稲田大学西早稲田キャンパス54号館101

 

題目:Hypergeometric functions and integrable hydrodynamic systems

 

講演者:Prof. Yuji Kodama (児玉裕治),  Ohio State University, USA

概要:I will show an interesting connection of (generalized) hypergeometric 
functions with integrable hydrodynamic-type systems. The lecture contains the following subjects.
(a) Integrable hydrodynamic systems generated by Lauricella functions.
(b) Confluence of the Lauricella functions and non-diagonalizable hydrodynamic-type systems.

 

 

9

日時:2017年6月6日火曜日 午後3時 − 午後6時

場所:早稲田大学西早稲田キャンパス51号館17-08

 

題目:KP solitons

 

講演者:Prof. Yuji Kodama (児玉裕治),  Ohio State University, USA

概要: I will discuss some combinatorial aspects of the KP solitons. This lecture is to explain the following subjects.
(a) Mathematical background of the regular soliton solutions (the totally non-negative Grassmannians and their parametrization).
(b) Applications of the KP solitons to shallow water waves (Mach reflection and rogue waves).

 

8

 

日時:2017年5月17日水曜日 午後3時 − 午後6時

場所:早稲田大学西早稲田キャンパス62W号館1階大会議室

 

題目:Riemann-Hilbert Methods in Integrable Systems II

Lecture  3: Asymptotic Analysis of Riemann-Hilbert Problems, Part I

Lecture  4: Asymptotic Analysis of Riemann-Hilbert Problems, Part II

 

講演者:Prof. Peter Miller, University of Michigan, USA

 

Lecture 3, Asymptotic Analysis of Riemann-Hilbert Problems, Part I: 

The Deift-Zhou steepest descent method is a powerful set of techniques applicable to Riemann-Hilbert problems that are generalizations of the classical steepest descent method for the asymptotic expansion of certain contour integrals.  This lecture will focus on the Fokas-Its'-Kitaev Riemann-Hilbert problem characterizing orthogonal polynomials with exponentially varying weights and the asymptotic limit of large degree as an example of the steepest descent method.  The goal of this lecture is to deform the Riemann-Hilbert problem to the point where it appears at a formal level to be asymptotically simple.  

Lecture 4, Asymptotic Analysis of Riemann-Hilbert Problems, Part II: 

This lecture picks up where Lecture 3 left off.  The deformed Riemann-Hilbert problem suggests an approximate solution, known as a parametrix.  The parametrix will be constructed explicitly with the help of elementary and special functions.  Then by comparing the parametrix to the exact solution we will arrive at a Riemann-Hilbert problem of small-norm type (cf., Lecture 2). Estimates on the solution of the latter problem yield explicit leading-order asymptotic formulae for the orthogonal polynomials and related quantities of interest in applications such as random matrix theory.  

 

7

日時:2017年5月16日火曜日 午後3時 − 午後6時

場所:早稲田大学西早稲田キャンパス62W号館1階大会議室

 

題目:Riemann-Hilbert Methods in Integrable Systems I

Lecture  1: Riemann-Hilbert Problems and Lax Pairs

Lecture  2: Some Theory of Riemann-Hilbert Problems

 

講演者:Prof. Peter Miller, University of Michigan, USA

 

Lecture 1, Riemann-Hilbert Problems and Lax Pairs: 

The inverse-scattering transform can be used to study the initial-value problem for certain nonlinear wave equations, and the most important part of this analysis frequently leads to a Riemann-Hilbert problem of complex function theory.  This lecture will explain how Riemann-Hilbert problems arise in this setting, and will then reveal why Riemann-Hilbert problems are fundamentally related to integrability by means of Lax pairs arising from the dressing construction. 

 

Lecture 2, Some Theory of Riemann-Hilbert Problems: 

A Riemann-Hilbert problem is fundamentally a problem of complex analysis, a kind of boundary-value problem for the Cauchy-Riemann equations.  However, as with many problems of elliptic partial differential equations, a Riemann-Hilbert problem can be recast as a singular integral equation.  This lecture will highlight some of the key ideas of the connection between Riemann-Hilbert problems and integral equations, with emphasis on the small-norm setting and how to achieve it by deformation techniques.

 

6

日時:2016年5月17日火曜日 午後1時00分 − 午後2時30分

場所:早稲田大学西早稲田キャンパス62W号館1階大会議室

 

題目:Unidirectional wave propagation and integrable models in shallow water

 

講演者:Prof. Roberto Camassa, University of North Carolina, USA

 

日時:2016年5月17日火曜日 午後245分 − 午後415

場所:早稲田大学西早稲田キャンパス62W号館1階大会議室

 

題目:Periodic waves and stability in deep water

 

講演者;Prof. Wooyoung Choi,  New Jersey Institute of Technology, USA

 

 

5

日時:2016年5月16日月曜日 午後1時00分 − 午後2時30分

場所:早稲田大学西早稲田キャンパス62W号館1階大会議室

 

題目:Fundamentals of fluid mechanics and free surface flows

 

講演者;Prof. Roberto Camassa, University of North Carolina, USA

 

日時:2016年5月16日月曜日 午後245分 − 午後415

場所:早稲田大学西早稲田キャンパス62W号館1階大会議室

 

題目:Asymptotic theories for nonlinear water waves

 

講演者:Prof. Wooyoung Choi,  New Jersey Institute of Technology, USA

 

4

日時:2015年3月16日月曜日 午後3時00分 − 午後5時00分

場所:早稲田大学西早稲田キャンパス62W号館1階大会議室

 

題目:From Schlesinger Transformations to Difference Painlevé Equations

 

講演者;Prof. Anton Dzhamay, School of Mathematical Sciences, University of Northern Colorado, USA

 

 

3

日時:2014年7月25日金曜日 午後時30分 − 午後6時00分

場所:早稲田大学西早稲田キャンパス63号館1階数学応数会議室

 

題目:Triangulations of convex polygon and solitons in 2-dimension

講演者;Prof. Yuji Kodama, Department of Mathematics, Ohio State University, USA

 

2

日時:2014年7月25日金曜日 午後時45分 − 午後4時15分

場所:早稲田大学西早稲田キャンパス63号館1階数学応数会議室

 

題目:Beach waves and line-solitons of the KP equation

講演者:Prof. Sarbarish Chakravarty, Department of Mathematics, The University of Colorado at Colorado Springs, USA

 

1

日時:2014年5月22日木曜日 午後時 − 午後6時30分

場所:早稲田大学西早稲田キャンパス62W号館1階大会議室

 

題目:The complex and coupled complex short pulse equations, their integrable discretizations and novel numerical simulations

講演者:Prof. Baofeng Feng, Department of Mathematics, The University of Texas Pan American, USA

 

 

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