Darboux transformation and two-dimensional Toda lattice

1983 ◽  
Vol 23 (4) ◽  
pp. 2441-2446 ◽  
Author(s):  
V. B. Matveev ◽  
M. A. Salle
Keyword(s):  
Darboux Transformation ◽  
Toda Lattice ◽  
Two Dimensional

A Transformation Connecting the Two-Dimensional Toda Lattice and K-dV Equation

1988 ◽  
Vol 57 (8) ◽  
pp. 2685-2688 ◽  
Author(s):  
Michiaki Matsukawa ◽  
Shinsuke Watanabe
Keyword(s):  
Toda Lattice ◽  
Two Dimensional

A generalized integrable hierarchy related to the relativistic Toda lattice: Hamiltonian structure, Darboux transformation, soliton solution and conservation law

2021 ◽  
Author(s):  
Zhiguo Xu
Keyword(s):  
Darboux Transformation ◽  
Hamiltonian Structure ◽  
Toda Lattice ◽  
Soliton Solutions ◽  
Integrable Hierarchy ◽  
Integrable Lattice ◽  
Pass Through ◽  
Matrix Spectral Problem ◽  
Relativistic Toda Lattice ◽  
Toda Lattice Hierarchy

Starting from a more generalized discrete [Formula: see text] matrix spectral problem and using the Tu scheme, some integrable lattice hierarchies (ILHs) are presented which include the well-known relativistic Toda lattice hierarchy and some new three-field ILHs. Taking one of the hierarchies as example, the corresponding Hamiltonian structure is constructed and the Liouville integrability is illustrated. For the first nontrivial lattice equation in the hierarchy, the [Formula: see text]-fold Darboux transformation (DT) of the system is established basing on its Lax pair. By using the obtained DT, we generate the discrete [Formula: see text]-soliton solutions in determinant form and plot their figures with proper parameters, from which we get some interesting soliton structures such as kink and anti-bell-shaped two-soliton, kink and anti-kink-shaped two-soliton and so on. These soliton solutions are much stable during the propagation, the solitary waves pass through without change of shapes, amplitudes, wave-lengths and directions. Finally, we derive infinitely many conservation laws of the system and give the corresponding conserved density and associated flux formulaically.

scholarly journals Five-Dimensional Gauge Theories and Whitham–Toda Equation

1997 ◽  
Vol 12 (29) ◽  
pp. 2183-2191 ◽  
Author(s):  
Masato Hisakado
Keyword(s):  
Gauge Theory ◽  
Toda Lattice ◽  
Gauge Theories ◽  
Toda Chain ◽  
Charge Conjugation ◽  
Two Dimensional ◽  
Toda Equation ◽  
Toda Lattice Hierarchy

The five-dimensional supersymmetric SU (N) gauge theory is studied in the framework of the relativistic Toda chain. This equation can be embedded in two-dimensional Toda lattice hierarchy. This system has the conjugate structure which corresponds to the charge conjugation.

scholarly journals Two-dimensional generalized Toda lattice

1981 ◽  
Vol 79 (4) ◽  
pp. 473-488 ◽  
Author(s):  
A. V. Mikhailov ◽  
M. A. Olshanetsky ◽  
A. M. Perelomov
Keyword(s):  
Toda Lattice ◽  
Two Dimensional

scholarly journals Two-Dimensional Toda Lattice Equations

1988 ◽  
Vol 94 ◽  
pp. 42-58 ◽  
Author(s):  
Ryogo Hirota ◽  
Masaaki Ito ◽  
Fujio Kako
Keyword(s):  
Toda Lattice ◽  
Two Dimensional ◽  
Toda Lattice Equations
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