A Darboux transformation and an exact solution for the relativistic Toda lattice equation

2005 ◽  
Vol 38 (35) ◽  
pp. 7735-7742 ◽  
Author(s):  
Ruguang Zhou ◽  
Qiaoyun Jiang
Keyword(s):  
Exact Solution ◽  
Darboux Transformation ◽  
Toda Lattice ◽  
Lattice Equation ◽  
Relativistic Toda Lattice ◽  
Toda Lattice Equation

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.

DARBOUX TRANSFORMATION OF THE MODIFIED TODA LATTICE EQUATION

2006 ◽  
Vol 20 (11) ◽  
pp. 641-648 ◽  
Author(s):  
XI-XIANG XU ◽  
HONG-XIANG YANG ◽  
YE-PENG SUN
Keyword(s):  
Spectral Problem ◽  
Soliton Solution ◽  
Darboux Transformation ◽  
Toda Lattice ◽  
Lattice Equation ◽  
Matrix Spectral Problem ◽  
Toda Lattice Equation

A modified Toda lattice equation associated with a properly discrete matrix spectral problem is introduced. Darboux transformation for the resulting lattice equation is constructed. As an application, the soliton solution for the Toda lattice equation is explicitly given.

N-SOLITON SOLUTIONS AND CONSERVATION LAWS OF THE MODIFIED TODA LATTICE EQUATION

2012 ◽  
Vol 26 (06) ◽  
pp. 1150032 ◽  
Author(s):  
XIAO-YONG WEN
Keyword(s):  
Conservation Laws ◽  
Darboux Transformation ◽  
Toda Lattice ◽  
Soliton Solutions ◽  
Lax Representation ◽  
Lattice Equation ◽  
Interaction Behavior ◽  
Toda Lattice Equation

The modified Toda lattice equation is investigated via Darboux transformation (DT) technique, the N-fold DT is constructed based on its Lax representation. The N-soliton solutions are also derived via the resulting N-fold DT. Soliton structures and interaction behavior of those solutions are shown graphically. Finally, the infinitely many conservation laws for that system are given.

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