A soliton cellular automaton associated with crystals of symmetric tensor representations of the quantum affine algebra U′q(A(1)M) is introduced. It is a crystal theoretic formulation of the generalized box-ball system in which capacities of boxes and carriers are arbitrary and inhomogeneous. Scattering matrices of two solitons coincide with the combinatorial R matrices of U′q(A(1)M-1). A piecewise linear evolution equation of the automaton is identified with an ultradiscrete limit of the nonautonomous discrete Kadomtsev-Petviashivili equation. A class of N soliton solutions is obtained through the ultradiscretization of soliton solutions of the latter.
All Science Journal Classification (ASJC) codes
- Statistical and Nonlinear Physics
- Mathematical Physics