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

N1 - Funding Information:
Acknowledgement. The author would like to thank the referee for his careful reading of the manuscript and his suggestions to make the paper more readable. The support from the Simons Foundation through Grant # 278994 is gratefully acknowledged.
Publisher Copyright:
© 2018, Springer-Verlag GmbH Germany, part of Springer Nature.
Copyright:
Copyright 2018 Elsevier B.V., All rights reserved.

PY - 2018/7/1

Y1 - 2018/7/1

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

VL - 361

SP - 415

EP - 466

JO - Communications in Mathematical Physics

JF - Communications in Mathematical Physics

SN - 0010-3616

IS - 2

ER -