25 research outputs found
On the initial value problem of a periodic box-ball system
We show that the initial value problem of a periodic box-ball system can be
solved in an elementary way using simple combinatorial methods.Comment: 9 pages, 2 figure
Correlation function for a periodic box-ball system
We investigate correlation functions in a periodic box-ball system. For the
two point functions of short distance, we give explicit formulae obtained by
combinatorial methods. We give expressions for general N-point functions in
terms of ultradiscrete theta functions.Comment: 13 pages, 2 figures, submitted to J. Phys. A: Math. Theo
Discrete Integrable Equations over Finite Fields
Discrete integrable equations over finite fields are investigated. The
indeterminacy of the equation is resolved by treating it over a field of
rational functions instead of the finite field itself. The main discussion
concerns a generalized discrete KdV equation related to a Yang-Baxter map.
Explicit forms of soliton solutions and their periods over finite fields are
obtained. Relation to the singularity confinement method is also discussed