scholarly journals Sato theory on the q-Toda hierarchy and its extension

2015 ◽  
Vol 76 ◽  
pp. 10-23 ◽  
Author(s):  
Chuanzhong Li
Keyword(s):  
Toda Hierarchy ◽  
Sato Theory

scholarly journals DISPERSIONLESS BIGRADED TODA HIERARCHY AND ITS ADDITIONAL SYMMETRY

2012 ◽  
Vol 24 (07) ◽  
pp. 1230003 ◽  
Author(s):  
CHUANZHONG LI ◽  
JINGSONG HE
Keyword(s):  
Additional Symmetry ◽  
Tau Function ◽  
Toda Hierarchy ◽  
Definition Of ◽  
Sato Theory ◽  
Bilinear Equations

In this paper, we firstly give the definition of dispersionless bigraded Toda hierarchy (dBTH) and introduce some Sato theory on dBTH. Then we define Orlov–Schulman's [Formula: see text], [Formula: see text] operator and give the additional Block symmetry of dBTH. Meanwhile we give tau function of dBTH and some related dispersionless bilinear equations.

Non-local integrable equations as reductions of the Toda hierarchy

1991 ◽  
Vol 160 (2) ◽  
pp. 166-172 ◽  
Author(s):  
D. Lebedev ◽  
A. Orlov ◽  
S. Pakuliak ◽  
A. Zabrodin
Keyword(s):  
Integrable Equations ◽  
Toda Hierarchy ◽  
Non Local

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 An Elementary Introduction to Sato Theory

1988 ◽  
Vol 94 ◽  
pp. 210-241 ◽  
Author(s):  
Yasuhiro Ohta ◽  
Junkichi Satsuma ◽  
Daisuke Takahashi ◽  
Tetsuji Tokihiro
Keyword(s):  
Sato Theory

The q-deformed mKP hierarchy with two parameters

2018 ◽  
Vol 32 (16) ◽  
pp. 1850170
Author(s):  
Kelei Tian ◽  
Yanyan Ge ◽  
Xiaoming Zhu
Keyword(s):  
Additional Symmetry ◽  
Lax Equation ◽  
Quantum Calculus ◽  
Two Parameters ◽  
Sato Theory

In this paper, with the help of the biparametric quantum calculus we construct the Sato theory on the q-deformation modified Kadomtsev–Petviashvili hierarchy with two parameters (qp-mKP), which is a new deformation of classical mKP hierarchy. The Lax equation and dressing operator of qp-mKP hierarchy are derived. By considering the M operator and [Formula: see text] operator, the additional symmetry of qp-mKP hierarchy is obtained.

scholarly journals QUASI-PERIODIC SOLUTIONS OF THE RELATIVISTIC TODA HIERARCHY

2012 ◽  
Vol 19 (04) ◽  
pp. 1250030 ◽  
Author(s):  
DONG GONG ◽  
XIANGUO GENG
Keyword(s):  
Meromorphic Function ◽  
Periodic Solutions ◽  
Continuous Flow ◽  
Hyperelliptic Curve ◽  
Algebraic Curves ◽  
Asymptotic Properties ◽  
Toda Hierarchy ◽  
Discrete Flow

On the basis of the theory of algebraic curves, the continuous flow and discrete flow related to the relativistic Toda hierarchy are straightened out using the Abel–Jacobi coordinates. The meromorphic function and the Baker–Akhiezer function are introduced on the hyperelliptic curve. Quasi-periodic solutions of the relativistic Toda hierarchy are constructed with the help of the asymptotic properties and the algebro-geometric characters of the meromorphic function and the hyperelliptic curve.

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