scholarly journals Integrable Toda system as a quantum approximation to the anisotropy of the mixmaster universe

2018 ◽  
Vol 98 (8) ◽  
Author(s):  
Hervé Bergeron ◽  
Ewa Czuchry ◽  
Jean-Pierre Gazeau ◽  
Przemysław Małkiewicz
Keyword(s):  
Toda System ◽  
Quantum Approximation

scholarly journals Analytic aspects of the Toda system: II. Bubbling behavior and existence of solutions

2006 ◽  
Vol 59 (4) ◽  
pp. 526-558 ◽  
Author(s):  
Jürgen Jost ◽  
Changshou Lin ◽  
Guofang Wang
Keyword(s):  
Existence Of Solutions ◽  
Toda System

On the Full-Discrete Extended Generalised q-Difference Toda System

2017 ◽  
Vol 72 (8) ◽  
pp. 703-709
Author(s):  
Chuanzhong Li ◽  
Anni Meng
Keyword(s):  
Difference Equation ◽  
Hamiltonian Structure ◽  
Soliton Solutions ◽  
Toda Equation ◽  
Lax Pairs ◽  
Toda System ◽  
Toda Hierarchy

AbstractIn this paper, we construct a full-discrete integrable difference equation which is a full-discretisation of the generalised q-Toda equation. Meanwhile its soliton solutions are constructed to show its integrable property. Further the Lax pairs of an extended generalised full-discrete q-Toda hierarchy are also constructed. To show the integrability, the bi-Hamiltonian structure and tau symmetry of the extended full-discrete generalised q-Toda hierarchy are given.

scholarly journals Degree counting for Toda system with simple singularity: One point blow up

2020 ◽  
Vol 268 (5) ◽  
pp. 2163-2209 ◽  
Author(s):  
Youngae Lee ◽  
Chang-Shou Lin ◽  
Wen Yang ◽  
Lei Zhang
Keyword(s):  
Blow Up ◽  
Simple Singularity ◽  
Toda System

scholarly journals WHITHAM DEFORMATIONS OF SEIBERG–WITTEN CURVES FOR CLASSICAL GAUGE GROUPS

2000 ◽  
Vol 15 (23) ◽  
pp. 3635-3666 ◽  
Author(s):  
KANEHISA TAKASAKI
Keyword(s):  
Spectral Curve ◽  
Explicit Construction ◽  
Integrable Hierarchy ◽  
Fractional Powers ◽  
Toda System ◽  
Gauge Groups ◽  
Yang Mills

Gorsky et al. presented an explicit construction of Whitham deformations of the Seiberg–Witten curve for the [Formula: see text] SUSY Yang–Mills theory. We extend their result to all classical gauge groups and some other cases such as the spectral curve of the [Formula: see text] affine Toda system. Our construction, too, uses fractional powers of the superpotential W(x) that characterizes the curve. We also consider the u-plane integral of topologically twisted theories on four-dimensional manifolds X with [Formula: see text] in the language of these explicitly constructed Whitham deformations and an integrable hierarchy of the KdV type hidden behind.

scholarly journals QuantumR matrix for the generalized Toda system

1986 ◽  
Vol 102 (4) ◽  
pp. 537-547 ◽  
Author(s):  
Michio Jimbo
Keyword(s):  
Toda System
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