Bäcklund transformation solutions of the Toda lattice equation

1975 ◽  
Vol 16 (7) ◽  
pp. 1428-1430 ◽  
Author(s):  
Hsing‐Hen Chen ◽  
Chuan‐Sheng Liu
Keyword(s):  
Toda Lattice ◽  
Bäcklund Transformation ◽  
Backlund Transformation ◽  
Lattice Equation ◽  
Toda Lattice Equation

scholarly journals AN APPLICATION OF THE CASORATIAN TECHNIQUE TO THE 2D TODA LATTICE EQUATION

2008 ◽  
Vol 22 (19) ◽  
pp. 1815-1825 ◽  
Author(s):  
WEN-XIU MA
Keyword(s):  
Toda Lattice ◽  
Bäcklund Transformation ◽  
Backlund Transformation ◽  
Lattice Equation ◽  
Toda Lattice Equation

A general Casoratian formulation is proposed for the 2D Toda lattice equation, which involves two coupled eigenfunction systems. Various Casoratian type solutions are generated, through solving the resulting linear conditions and using a Bäcklund transformation.

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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