Bethe ansatz and inverse scattering transform in a periodic box-ball system

Details Bethe ansatz and inverse scattering transform in a periodic box-ball system Bethe ansatz and inverse scattering transform in a periodic box-ball system

2006-02-22

arxiv.org/abs/math/0602481v2

Nucl. Phys. B747[PM] (2006) 354-397

Mathematics

Quantum Algebra

43 pages

Scientific paper

10.1016/j.nuclphysb.2006.04.003

We formulate the inverse scattering method for a periodic box-ball system and solve the initial value problem. It is done by a synthesis of the combinatorial Bethe ansa"tze at q=1 and q=0, which provides the ultradiscrete analogue of quasi-periodic solutions in soliton equations, e.g., action-angle variables, Jacobi varieties, period matrices and so forth. As an application we establish explicit formulas counting the states characterized by conserved quantities and the generic and fundamental period under the commuting family of time evolutions.

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