An Exact Discretization of a Lax Equation for Shock Clustering and Burgers Turbulence I: Dynamical Aspects and Exact Solvability

2018 ◽  
Vol 361 (2) ◽  
pp. 415-466 ◽  
Author(s):  
Luen-Chau Li
Keyword(s):  
Lax Equation ◽  
Exact Solvability ◽  
Burgers Turbulence

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.

Burgers Turbulence and Dynamical Systems

2001 ◽  
pp. 429-443
Author(s):  
Renato Iturriaga ◽  
Konstantin Khanin
Keyword(s):  
Dynamical Systems ◽  
Burgers Turbulence

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.

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