Integrability analysis of regular and fractional Blackmore-Samulyak-Rosato fields

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.