## Abstract

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.

Original language | English |
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Pages (from-to) | 274-308 |

Number of pages | 35 |

Journal | Journal of Mathematical Physics |

Volume | 42 |

Issue number | 1 |

DOIs | |

Publication status | Published - Jan 2001 |

Externally published | Yes |

## All Science Journal Classification (ASJC) codes

- Statistical and Nonlinear Physics
- Mathematical Physics