Matrix Integral Solutions to the q-Difference Two-Dimensional Toda Lattice Equation and Its Pfaffianized System

2019 ◽  
Vol 88 (12) ◽  
pp. 124003
Author(s):  
Chun-Xia Li ◽  
Zhen-Yun Qin ◽  
Shou-Feng Shen
Keyword(s):  
Toda Lattice ◽  
Two Dimensional ◽  
Lattice Equation ◽  
Matrix Integral ◽  
Toda Lattice Equation ◽  
Integral Solutions

On integrability of a noncommutative q -difference two-dimensional Toda lattice equation

2015 ◽  
Vol 379 (47-48) ◽  
pp. 3075-3083 ◽  
Author(s):  
C.X. Li ◽  
J.J.C. Nimmo ◽  
Shoufeng Shen
Keyword(s):  
Toda Lattice ◽  
Two Dimensional ◽  
Lattice Equation ◽  
Toda Lattice Equation

scholarly journals Coprimeness-preserving non-integrable extension to the two-dimensional discrete Toda lattice equation

2017 ◽  
Vol 58 (1) ◽  
pp. 012702 ◽  
Author(s):  
Ryo Kamiya ◽  
Masataka Kanki ◽  
Takafumi Mase ◽  
Tetsuji Tokihiro
Keyword(s):  
Toda Lattice ◽  
Two Dimensional ◽  
Lattice Equation ◽  
Toda Lattice Equation

SU(N) LIE ALGEBRA, EXTENDED TODA LATTICE EQUATION AND THE EXACT SOLUTIONS

1994 ◽  
Vol 09 (06) ◽  
pp. 525-534
Author(s):  
A. ROY CHOWDHURY ◽  
A. GHOSE CHOUDHURY
Keyword(s):  
Exact Solutions ◽  
Lie Algebra ◽  
Toda Lattice ◽  
Two Dimensional ◽  
Lattice Equation ◽  
Curvature Equation ◽  
Zero Curvature ◽  
Dimensional Gravity ◽  
Differential Generalization ◽  
Toda Lattice Equation

An integro-differential generalization of the Toda lattice equation is proposed via the zero curvature equation belonging to SU(N) Lie algebra. It is shown that the exact solutions for this equation can be constructed by the method of chiral vectors. Explicit results are given for SU(2) and SU(3). We also demonstrate that these equations are connected to the constrained WZW theory and hence Polyakov’s two-dimensional gravity.

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