Bernoulli product measures are invariant for BBS-S(2) and BBS-V(2), while two-sided Markov distributions are invariant for BBS-C(2), with phase shifts and velocities computed for all three Mealy-automaton soliton models.
Doyon, Generalized hydrodynamics of the classical Toda system, Journal of Mathematical Physics60, 073302 (2019)
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Invariant Measures for Soliton Systems Generated by Mealy Automata
Bernoulli product measures are invariant for BBS-S(2) and BBS-V(2), while two-sided Markov distributions are invariant for BBS-C(2), with phase shifts and velocities computed for all three Mealy-automaton soliton models.