### 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 language | English (US) |
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Pages (from-to) | 1-52 |

Number of pages | 52 |

Journal | Communications in Mathematical Physics |

DOIs | |

State | Accepted/In press - Jun 18 2018 |

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### All Science Journal Classification (ASJC) codes

- Statistical and Nonlinear Physics
- Mathematical Physics

### Cite this

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**An Exact Discretization of a Lax Equation for Shock Clustering and Burgers Turbulence I : Dynamical Aspects and Exact Solvability.** / Li, Luen-chau.

Research output: Contribution to journal › Article

TY - JOUR

T1 - An Exact Discretization of a Lax Equation for Shock Clustering and Burgers Turbulence I

T2 - Dynamical Aspects and Exact Solvability

AU - Li, Luen-chau

PY - 2018/6/18

Y1 - 2018/6/18

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=85048699703&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85048699703&partnerID=8YFLogxK

U2 - 10.1007/s00220-018-3179-8

DO - 10.1007/s00220-018-3179-8

M3 - Article

AN - SCOPUS:85048699703

SP - 1

EP - 52

JO - Communications in Mathematical Physics

JF - Communications in Mathematical Physics

SN - 0010-3616

ER -