scholarly journals The Elliptic Painlevé Lax Equation vs. van Diejen's 8-Coupling Elliptic Hamiltonian

2020 ◽  
Author(s):  
Masatoshi Noumi ◽  
◽  
Simon Ruijsenaars ◽  
Yasuhiko Yamada ◽  
◽  
...  
Keyword(s):  
Lax Equation

Intrinsic geometry of Lax equation

2003 ◽  
Vol 6 (3) ◽  
pp. 291-299
Author(s):  
Carlo Cattani ◽  
Ettore Laserra
Keyword(s):  
Intrinsic Geometry ◽  
Lax Equation

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.

The q-deformed mKP hierarchy with two parameters

2018 ◽  
Vol 32 (16) ◽  
pp. 1850170
Author(s):  
Kelei Tian ◽  
Yanyan Ge ◽  
Xiaoming Zhu
Keyword(s):  
Additional Symmetry ◽  
Lax Equation ◽  
Quantum Calculus ◽  
Two Parameters ◽  
Sato Theory

In this paper, with the help of the biparametric quantum calculus we construct the Sato theory on the q-deformation modified Kadomtsev–Petviashvili hierarchy with two parameters (qp-mKP), which is a new deformation of classical mKP hierarchy. The Lax equation and dressing operator of qp-mKP hierarchy are derived. By considering the M operator and [Formula: see text] operator, the additional symmetry of qp-mKP hierarchy is obtained.

scholarly journals Zero Curvature Formalism for Supersymmetric Integrable Hierarchies in Superspace

1997 ◽  
Vol 12 (34) ◽  
pp. 2623-2630 ◽  
Author(s):  
H. Aratyn ◽  
C. Rasinariu ◽  
A. Das
Keyword(s):  
Symmetric Space ◽  
Integrable Systems ◽  
Integrable Hierarchies ◽  
Space Structure ◽  
Hermitian Symmetric Space ◽  
Curvature Condition ◽  
Lax Equation ◽  
Abelian Gauge ◽  
Graded Algebras ◽  
Zero Curvature

We generalize the Drinfeld–Sokolov formalism of bosonic integrable hierarchies to superspace, in a way which systematically leads to the zero curvature formulation for the supersymmetric integrable systems starting from the Lax equation in superspace. We use the method of symmetric space as well as the non-Abelian gauge technique to obtain the supersymmetric integrable hierarchies of the AKNS type from the zero curvature condition in superspace with the graded algebras, sl (n+1,n), providing the Hermitian symmetric space structure.

On generalized Lax equation of the Lax triple of mKP hierarchy

2020 ◽  
Vol 35 (20) ◽  
pp. 2050099
Author(s):  
Chong Li ◽  
Lin-Jie Shi ◽  
Xiao-Li Wang ◽  
Na Wang ◽  
Min-Ru Chen
Keyword(s):  
Lax Pair ◽  
Lax Equation

Based on the Lax pair [Formula: see text] of the mKP hierarchy and the operator Nambu 3-bracket, we propose the generalized Lax equation with respect to the Lax triple [Formula: see text]. For different pairs [Formula: see text] in the generalized Lax equation, a generalized hierarchy including the mKP hierarchy is derived.

ALGEBRAIC STUDY ON THE POISSON STRUCTURE OF LAX OPERATOR OF B AND C TYPE AND SUPER LAX OPERATOR.

1992 ◽  
Vol 07 (supp01a) ◽  
pp. 405-418
Author(s):  
KAORU IKEDA
Keyword(s):  
Poisson Structure ◽  
Algebraic Structure ◽  
Lax Equation ◽  
Lax Operator

The Poisson structure of Lax operator of B and C type and super Lax operator which has odd parity are studied. The algebraic structure of Poisson structure as a background of Lax equation is thrown light on.

CANONICAL BÄCKLUND TRANSFORMATION FOR A DISCRETE INTEGRABLE CHAIN AND ITS ASSOCIATED PROPERTIES

2003 ◽  
Vol 18 (16) ◽  
pp. 1127-1139
Author(s):  
A. GHOSE CHOUDHURY ◽  
BARUN KHANRA ◽  
A. ROY CHOWDHURY
Keyword(s):  
Poisson Structure ◽  
Algebraic Structure ◽  
Bäcklund Transformation ◽  
Inverse Transformation ◽  
Strict Sense ◽  
Backlund Transformation ◽  
Lax Equation ◽  
R Matrix ◽  
Lax Operator ◽  
Time Part

The concept of a canonical Bäcklund transformation as laid down by Sklyanin is extended to a discrete integral chain, with a Poisson structure which is not canonical in the strict sense. The transformation is induced by an auxiliary Lax operator with a classical r-matrix which is similar in its algebraic structure to that of the original Lax operator governing the dynamics of the chain. Moreover, the transformation can be obtained from a suitable generating function. It is also shown how successive transformations can be composed to construct a new transformation. Finally an inverse transformation is also constructed. The compatibility of the transformation with the "time" part of the Lax equation is explicitly demonstrated. It is also shown that the Bianchi theorem of permutability holds good.

Additive generalizations of the lax equation

2001 ◽  
Vol 48 (3) ◽  
pp. 425-440
Author(s):  
Maria Przybylska
Keyword(s):  
Lax Equation

scholarly journals A NONSTANDARD SUPERSYMMETRIC KP HIERARCHY

1995 ◽  
Vol 07 (08) ◽  
pp. 1181-1194 ◽  
Author(s):  
J.C. BRUNELLI ◽  
A. DAS
Keyword(s):  
Schrödinger Equation ◽  
Nonlinear Schrödinger Equation ◽  
Schrodinger Equation ◽  
Mkdv Equation ◽  
Nonlinear Schrodinger Equation ◽  
Kp Equation ◽  
Kp Hierarchy ◽  
Lax Equation ◽  
Conserved Charges ◽  
Nonlinear Schrödinger

We show that the supersymmetric nonlinear Schrödinger equation can be written as a constrained super KP flow in a nonstandard representation of the Lax equation. We construct the conserved charges and show that this system reduces to the super mKdV equation with appropriate identifications. We construct various flows generated by the general nonstandard super Lax equation and show that they contain both the KP and mKP flows in the bosonic limits. This nonstandard supersymmetric KP hierarchy allows us to construct a new super KP equation which is nonlocal.

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