On the integrability problem of a continuous Toda system

1992 ◽  
Vol 92 (3) ◽  
pp. 1024-1031 ◽  
Author(s):  
M. V. Saveliev
Keyword(s):  
Toda System ◽  
Integrability Problem

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 On the integrability problem for systems of partial differential equations in one unknown function, I

2019 ◽  
Vol 11 (4) ◽  
pp. 35-71 ◽  
Author(s):  
Antonio Kumpera
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Unknown Function ◽  
Contact Structures ◽  
Partial Differential ◽  
Practical Applications ◽  
First Order ◽  
Integrability Problem ◽  
Integration Problem ◽  
In The Beginning

We discuss the integration problem for systems of partial differential equations in one unknown function and special attention is given to the first order systems. The Grassmannian contact structures are the basic setting for our discussion and the major part of our considerations inquires on the nature of the Cauchy characteristics in view of obtaining the necessary criteria that assure the existence of solutions. In all the practical applications of partial differential equations, what is mostly needed and what in fact is hardest to obtains are the solutions of the system or, occasionally, some specific solutions. This work is based on four most enlightening Mémoires written by Élie Cartan in the beginning of the last century.

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.

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