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Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Rational solutions of KP and BKP hierarchies through Toda lattice
户田晶格 KP BKP 层次结构 合理解
2023/4/27
The full Kostant-Toda lattice defined on simple Lie algebras can be viewed as finite version of KP type hierarchies. In this talk I will show you how to explicitly construct (all) rational solutions o...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：A unified method to construct soliton solutions to NLS type equations by the KP-Toda reduction approach: Part II discrete case
KP-户田约简法 NLS类型 方程孤子解 统一方法 离散情况
2023/4/27
In the second part, I will mainly focus on two semi-discrete models: Ablowitz-Ladik equation and fully discrete NLS equation. First, I will clarify the connection of these two discrete models with dis...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：A unified method to construct soliton solutions to NLS type equations by the KP-Toda reduction approach: Part I continuous case
KP-户田约简法 NLS类型 方程孤子解 统一方法 离散情况
2023/4/27
In these two talks, I will present a unified method to construct soliton solutions to NLS type equations by the KP-Toda reduction approach. I will take the NLS equation as a typical example and show h...
尖峰孤子、Toda格和相关谱问题
尖峰孤子 Toda格方程 相关谱
2021/8/18
Camassa-Holm（CH）方程自二十世纪九十年代被Camassa和Holm研究浅水波模型时发现以来，由于具有一些重要特性引起了许多数学家和物理学家的关注和兴趣，其中一个最显著的特点是存在一类尖峰孤子解，即一种有尖点但和光滑孤立子一样具有碰撞后不改变其形状和速度等性质的特解，因此促使许多学者研究尖峰孤子及其性质。尖峰孤子不仅具有丰富的数学结构，对其的研究也有助于理解波破裂现象。
Toda方程的渐近行为
Toda方程 渐近行为 Allen-Cahn方程
2014/1/9
利用Toda方程中的指数势函数的性质，讨论了Toda方程解在无穷远处的渐近行为，证明了Toda方程的任何一个解在无穷远处是渐近线性的.
Old and new reductions of dispersionless Toda hierarchy
dispersionless Toda hierarchy finite-variable reduction waterbag model Landau-Ginzburg potential Lowner equations
2012/6/21
Two types of finite-variable reductions of the dispersionless Toda hierarchy are considered in the geometric perspectives. The reductions are formulated in terms of "Landau-Ginzburg potentials" that p...
The Algebro-Geometric Initial Value Problem for the Ruijsenaars-Toda Hierarchy and Quasi-Periodic Solutions
Ruijsenaars-Toda hierarchy complex-valued algebro-geometric solutions hyperelliptic curve Dubrovin-type equation Baker-Akhiezer vector
2012/4/27
We provide a detailed treatment of Ruijsenaars-Toda (RT) hierarchy with special emphasis on its the theta function representation of all algebro-geometric solutions. The basic tools involve hyperellip...
The Continuum Limit of Toda Lattices for Random Matrices with Odd Weights
Toda Lattices Continuum Limit Random Matrices Odd Weights
2011/7/7
This paper is concerned with the asymptotic behavior of the free energy for a class of Hermitean random matrix models, with odd degree polynomial potential, in the large N limit. It continues an inves...
The Continuum Limit of Toda Lattices for Random Matrices with Odd Weights
The Continuum Limit of Toda Lattices Random Matrices Odd Weights
2011/7/25
Abstract: This paper is concerned with the asymptotic behavior of the free energy for a class of Hermitean random matrix models, with odd degree polynomial potential, in the large N limit. It continue...
Toda Molecule and Tomimatsu-Sato Solution $\sim$ Toward the complete proof of Nakamura's conjecture$\sim$
Toda Molecule Tomimatsu-Sato Solution $\sim$ complete proof of Nakamura's conjecture$\sim$
2011/1/18
We discuss the Nakamura’s conjecture stating that the Tomimatsu-Sato black hole solution with deformation parameter n is composed of the special solutions of the Toda molecule equation at the n-th lat...
The Toda chains take a particular place in the theory of integrable systems,in contrast with the linear group structure for the Gaudin model this system is related to the corresponding Borel group and...
Integrable defects in affine Toda field theory and infinite dimensional representations of quantum groups
Integrable defects affine Toda field theory infinite dimensional representations quantum groups
2011/3/3
Transmission matrices for two types of integrable defect are calculated explicitly, first by solving directly the nonlinear transmission Yang-Baxter equations.
Toda Molecule and Tomimatsu-Sato Solution $\sim$ Toward the complete proof of Nakamura's conjecture$\sim$
Toda Molecule Tomimatsu-Sato Solution $\sim$
2010/12/28
We discuss the Nakamura’s conjecture stating that the Tomimatsu-Sato black hole solution with deformation parameter n is composed of the special solutions of the Toda molecule equation at the n-th lat...
The Toda chains take a particular place in the theory of integrable systems,in contrast with the linear group structure for the Gaudin model this system is related to the corresponding Borel group and...
The $(N,M)$-bigraded Toda hierarchy is an extension of the original Toda lattice hierarchy. The pair of numbers $(N,M)$ represents the band structure of the Lax matrix which has $N$ upper and $M$ lowe...