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 - Publisher Copyright:
© 2018, Springer-Verlag GmbH Germany, part of Springer Nature.

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.

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U2 - 10.1007/s00220-018-3179-8

DO - 10.1007/s00220-018-3179-8

M3 - Article

AN - SCOPUS:85048699703

SN - 0010-3616

VL - 361

SP - 415

EP - 466

JO - Communications In Mathematical Physics

JF - Communications In Mathematical Physics

IS - 2

ER -