Periodic Box-ball System Research Articles

Initial-value problem of the discrete periodic Toda equation and itsultradiscretization

An initial-value problem of the periodic discrete Toda equation is solved by theinverse scattering method. Using this result, we demonstrate a method for solvingan initial-value problem of a periodic box–ball system which is one of the typicalsoliton cellular automata. In the method, ultradiscretization and its inverseprocess play an essential role. The explicit solution to the case of genus one is alsopresented.