scholarly journals An extended two-dimensional Toda lattice hierarchy and two-dimensional Toda lattice with self-consistent sources

2008 ◽  
Vol 49 (9) ◽  
pp. 093506 ◽  
Author(s):  
Xiaojun Liu ◽  
Yunbo Zeng ◽  
Runliang Lin
Keyword(s):  
Toda Lattice ◽  
Two Dimensional ◽  
Self Consistent ◽  
Toda Lattice Hierarchy

scholarly journals Five-Dimensional Gauge Theories and Whitham–Toda Equation

1997 ◽  
Vol 12 (29) ◽  
pp. 2183-2191 ◽  
Author(s):  
Masato Hisakado
Keyword(s):  
Gauge Theory ◽  
Toda Lattice ◽  
Gauge Theories ◽  
Toda Chain ◽  
Charge Conjugation ◽  
Two Dimensional ◽  
Toda Equation ◽  
Toda Lattice Hierarchy

The five-dimensional supersymmetric SU (N) gauge theory is studied in the framework of the relativistic Toda chain. This equation can be embedded in two-dimensional Toda lattice hierarchy. This system has the conjugate structure which corresponds to the charge conjugation.

scholarly journals Faces of Relativistic Toda Chain

1997 ◽  
Vol 12 (15) ◽  
pp. 2675-2724 ◽  
Author(s):  
S. Kharchev ◽  
A. Mironov ◽  
A. Zhedanov
Keyword(s):  
Orthogonal Polynomial ◽  
Toda Lattice ◽  
Toda Chain ◽  
Polynomial Systems ◽  
Function Approach ◽  
Unitary Matrix ◽  
Lax Representation ◽  
Two Dimensional ◽  
Two Component ◽  
Toda Lattice Hierarchy

We demonstrate that the generalization of the relativistic Toda chain (RTC) is a special reduction of two-dimensional Toda lattice hierarchy (2DTL). This reduction implies that the RTC is gauge equivalent to the discrete AKNS hierarchy and, which is the same, to the two-component Volterra hierarchy while its forced (semi-infinite) variant is described by the unitary matrix integral. The integrable properties of the RTC hierarchy are revealed in different frameworks of the Lax representation, orthogonal polynomial systems, and τ-function approach. Relativistic Toda molecule hierarchy is also considered, along with the forced RTC. Some applications to biorthogonal polynomial systems are discussed.

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