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Renormalization of the τ‐functions for integrable systems: A model problem
Author(s) -
McDonald Michael A.,
Venakides Stephanos
Publication year - 1998
Publication title -
communications on pure and applied mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 3.12
H-Index - 115
eISSN - 1097-0312
pISSN - 0010-3640
DOI - 10.1002/(sici)1097-0312(199808)51:8<937::aid-cpa3>3.0.co;2-6
Subject(s) - integrable system , renormalization , mathematics , supercritical fluid , limit (mathematics) , mathematical physics , renormalization group , chain (unit) , function (biology) , order (exchange) , mathematical analysis , physics , quantum mechanics , thermodynamics , finance , evolutionary biology , biology , economics
We introduce a renormalization procedure for theτ‐function of integrable systems. We illustratethe procedure using the supercritical Toda shock problemas a model problem. We start with a finite chainand take the limit of the solutionas the number of particles N → ∞.This results in a new formula for the τ‐function for theproblem with an infinite chain. We apply the renormalizedformula to rederive leading‐order effectsof the supercritical Toda shock problem. © 1998 John Wiley & Sons, Inc.