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

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Abstract

We consider a finite dimensional system which arises as an exact discretization of the Lax equation for shock clustering, which describes the evolution of the generator of a Markov process with a finite number of states. The spectral curve of the system is a nodal curve which is fully reducible. In this work, we will show that the flow is conjugate to a straight line motion, and we will also show that the equation is exactly solvable. En route, we will establish a dictionary between an open, dense set of the lower triangular infinitesimal generator matrices and an associated set of algebro-geometric data.

Original languageEnglish (US)
Pages (from-to)1-52
Number of pages52
JournalCommunications in Mathematical Physics
DOIs
StateAccepted/In press - Jun 18 2018

Fingerprint

Lax Equation
Solvability
Turbulence
Shock
generators
Discretization
turbulence
shock
Clustering
Nodal Curve
Spectral Curve
dictionaries
Markov processes
Infinitesimal Generator
curves
Open set
Straight Line
Markov Process
Triangular
routes

All Science Journal Classification (ASJC) codes

  • Statistical and Nonlinear Physics
  • Mathematical Physics

Cite this

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