Condensed Matter Physics, 2010, vol. 13, No. 4, p. 43403:1-7

Title: Integrability analysis of regular and fractional Blackmore-Samulyak-Rosato fields
  D. Blackmore (Department of Mathematical Sciences and Center for Applied Mathematics and Statistics, New Jersey Institute of Technology Newark, NJ 07102-1982) ,
  K. Urban (Center for Solar-Terrestrial Research, New Jersey Institute of Technology, Newark, NJ 07102-1982) ,
  A. Rosato (Department of Mechanical Engineering, New Jersey Institute of Technology, Newark, NJ 07102-1982)

Blackmore-Samulyak-Rosato (BSR) fields, originally developed as a means of obtaining reliable continuum approximations for granular flow dynamics in terms of relatively simple integro-differential equations, can be used to model a wide range of physical phenomena. Owing to results obtained for one-dimensional granular flow configurations, it has been conjectured that BSR models of fields with perfectly elastic interactions are completely integrable infinite-dimensional Hamiltonian systems. This conjecture is proved for BSR models in one space dimension, and analogues of BSR fields involving fractional time derivatives are briefly investigated.

Key words: BSR model, bi-Hamiltonian, completely integrable, fractional derivative
PACS: 45.70.Mg, 47.10.Df,, 02.60.Nm

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