scholarly journals 2D Toda lattice equation with self-consistent sources: Casoratian type solutions, bilinear Bäcklund transformation and Lax pair

2007 ◽  
Vol 202 (1) ◽  
pp. 133-143 ◽  
Author(s):  
Hong-Yan Wang ◽  
Xing-Biao Hu ◽  
Gegenhasi
Keyword(s):  
Toda Lattice ◽  
Bäcklund Transformation ◽  
Lax Pair ◽  
Backlund Transformation ◽  
Lattice Equation ◽  
Bilinear Bäcklund Transformation ◽  
Self Consistent ◽  
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.

N-SOLITON-LIKE SOLUTIONS AND BÄCKLUND TRANSFORMATIONS FOR A NON-ISOSPECTRAL AND VARIABLE-COEFFICIENT MODIFIED KORTEWEG-DE VRIES EQUATION

2011 ◽  
Vol 25 (05) ◽  
pp. 723-733 ◽  
Author(s):  
QIAN FENG ◽  
YI-TIAN GAO ◽  
XIANG-HUA MENG ◽  
XIN YU ◽  
ZHI-YUAN SUN ◽  
...  
Keyword(s):  
Variable Coefficient ◽  
Vries Equation ◽  
Bäcklund Transformation ◽  
Lax Pair ◽  
Mkdv Equation ◽  
Wronskian Technique ◽  
Backlund Transformation ◽  
Bilinear Bäcklund Transformation ◽  
De Vries ◽  
Bilinear Equations

A non-isospectral and variable-coefficient modified Korteweg–de Vries (mKdV) equation is investigated in this paper. Starting from the Ablowitz–Kaup–Newell–Segur procedure, the Lax pair is established and the Bäcklund transformation in original variables is also derived. By a dependent variable transformation, the non-isospectral and variable-coefficient mKdV equation is transformed into bilinear equations, by virtue of which the N-soliton-like solution is obtained. In addition, the bilinear Bäcklund transformation gives a one-soliton-like solution from a vacuum one. Furthermore, the N-soliton-like solution in the Wronskian form is constructed and verified via the Wronskian technique.

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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