N-fold Darboux transformations and exact solutions of the combined Toda lattice and relativistic Toda lattice equation

2020 ◽  
Vol 10 (3) ◽  
Author(s):  
Fang-Cheng Fan ◽  
Zhi-Guo Xu ◽  
Shao-Yun Shi
Keyword(s):  
Exact Solutions ◽  
Toda Lattice ◽  
Darboux Transformations ◽  
Lattice Equation ◽  
Relativistic Toda Lattice ◽  
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.

scholarly journals Casorati determinant solution for the relativistic Toda lattice equation

1993 ◽  
Vol 34 (11) ◽  
pp. 5190-5204 ◽  
Author(s):  
Yasuhiro Ohta ◽  
Kenji Kajiwara ◽  
Junta Matsukidaira ◽  
Junkichi Satsuma
Keyword(s):  
Toda Lattice ◽  
Lattice Equation ◽  
Casorati Determinant ◽  
Relativistic Toda Lattice ◽  
Toda Lattice Equation

Bäcklund transformation for the first flows of the relativistic Toda hierarchy and associated properties

Open Physics ◽  
2013 ◽  
Vol 11 (1) ◽  
Author(s):  
Anindya Choudhury
Keyword(s):  
Generating Function ◽  
Toda Lattice ◽  
Bäcklund Transformation ◽  
Hamiltonian Formalism ◽  
Bäcklund Transformations ◽  
Lattice Equation ◽  
Toda Hierarchy ◽  
Relativistic Toda Lattice ◽  
Toda Lattice Equation ◽  
Parameter Dependent

AbstractIn this communication we study a class of one parameter dependent auto-Bäcklund transformations for the first flow of the relativistic Toda lattice and also a variant of the usual Toda lattice equation. It is shown that starting from the Hamiltonian formalism such transformations are canonical in nature with a well defined generating function. The notion of spectrality is also analyzed and the separation variables are explicitly constructed.

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