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) |
|---|---|
| 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
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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.
In: Communications in Mathematical Physics, 18.06.2018, p. 1-52.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 -