scholarly journals A q-generalization of the Toda equations for the q-Laguerre/Hermite orthogonal polynomials

2018 ◽  
Vol 07 (04) ◽  
pp. 1840002 ◽  
Author(s):  
Chuan-Tsung Chan ◽  
Hsiao-Fan Liu
Keyword(s):  
Orthogonal Polynomials ◽  
Deformation Theory ◽  
Toda Lattice ◽  
Quadratic Relation ◽  
Lax Equation ◽  
Toda Equations

Based on the motivation of generalizing the correspondence between the Lax equation for the Toda lattice and the deformation theory of the orthogonal polynomials, we derive a [Formula: see text]-deformed version of the Toda equations for both [Formula: see text]-Laguerre/Hermite ensembles, and check the compatibility with the quadratic relation.

scholarly journals Direct and inverse spectral transform for the relativistic Toda lattice and the connection with Laurent orthogonal polynomials

2002 ◽  
Vol 18 (3) ◽  
pp. 923-942 ◽  
Author(s):  
J Coussement ◽  
A B J Kuijlaars ◽  
W Van Assche
Keyword(s):  
Orthogonal Polynomials ◽  
Toda Lattice ◽  
Spectral Transform ◽  
Inverse Spectral ◽  
Relativistic Toda Lattice

scholarly journals Extended Relativistic Toda Lattice, L-Orthogonal Polynomials and Associated Lax Pair

2018 ◽  
Vol 164 (1) ◽  
pp. 137-154
Author(s):  
Cleonice F. Bracciali ◽  
Jairo S. Silva ◽  
A. Sri Ranga
Keyword(s):  
Orthogonal Polynomials ◽  
Toda Lattice ◽  
Lax Pair ◽  
Relativistic Toda Lattice

Direct and inverse problems for the generalized relativistic Toda lattice and the connection with general orthogonal polynomials

2008 ◽  
Vol 24 (2) ◽  
pp. 025009 ◽  
Author(s):  
A Gago-Alonso ◽  
L Santiago-Moreno ◽  
L R Piñeiro-Díaz
Keyword(s):  
Inverse Problems ◽  
Orthogonal Polynomials ◽  
Toda Lattice ◽  
Direct And Inverse Problems ◽  
Relativistic Toda Lattice

scholarly journals Explicit Solutions of Integrable Variable-coeffcient Cylindrical Toda Equations

2020 ◽  
pp. 1-9
Author(s):  
Ting Su ◽  
Jia Wang ◽  
Quan Zhen Huang
Keyword(s):  
Soliton Solution ◽  
Compatibility Condition ◽  
Toda Lattice ◽  
Soliton Solutions ◽  
Explicit Solutions ◽  
Dressing Method ◽  
New Type ◽  
Toda Equations ◽  
Toda Lattice Equations

Integrable cylindrical Toda lattice equations are proposed by utilizing a generalized version of the dressing method. A compatibility condition is given which insures that these equations are integrable. Further, soliton solutions for new type equations are shown in explicit forms, including one soliton solution and two soliton solutions, respectively.

scholarly journals Christoffel Transformations for Matrix Orthogonal Polynomials in the Real Line and the non-Abelian 2D Toda Lattice Hierarchy

2016 ◽  
pp. rnw027 ◽  
Author(s):  
Carlos Álvarez-Fernández ◽  
Gerardo Ariznabarreta ◽  
Juan Carlos García-Ardila ◽  
Manuel Mañas ◽  
Francisco Marcellán
Keyword(s):  
Orthogonal Polynomials ◽  
Real Line ◽  
Toda Lattice ◽  
The Real ◽  
Matrix Orthogonal Polynomials ◽  
Toda Lattice Hierarchy

scholarly journals On some geometry associated with a generalised Toda lattice

1994 ◽  
Vol 49 (3) ◽  
pp. 439-462 ◽  
Author(s):  
P.J. Vassiliou
Keyword(s):  
Field Theory ◽  
Toda Lattice ◽  
Differential Operators ◽  
Lax Pair ◽  
Darboux Integrability ◽  
Partial Differential Operators ◽  
Alternative Means ◽  
Image Position ◽  
Toda Equations ◽  
Toda Field Theory

We define the notion of Darboux integrability for linear second order partial differential operators,.We then build on certain geometric results of E. Vessiot related to the theory of Monge characteristics to show that the Darboux integrable operators L can be used to obtain a solution of the A2 Toda field theory. This solution is parametrised by four arbitrary functions. The approach presented in this paper thereby represents an alternative means of linearising the A2 Toda equations and may be contrasted with the known linearisation via the Lax pair.

scholarly journals On the relation between the full Kostant–Toda lattice and multiple orthogonal polynomials

2011 ◽  
Vol 377 (1) ◽  
pp. 228-238 ◽  
Author(s):  
D. Barrios Rolanía ◽  
A. Branquinho ◽  
A. Foulquié Moreno
Keyword(s):  
Orthogonal Polynomials ◽  
Toda Lattice ◽  
Multiple Orthogonal Polynomials

Orthogonal polynomials and the finite Toda lattice

1997 ◽  
Vol 38 (1) ◽  
pp. 247-254 ◽  
Author(s):  
Alex Kasman
Keyword(s):  
Orthogonal Polynomials ◽  
Toda Lattice
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