We study the soliton cellular automaton (SCA) in (2+1)-dimensions from the viewpoint of the integrable vertex model. As in our previous paper, we relate the SCA, the so-called box-ball system, to an integrable vertex model associated with the Bogoyavlensky lattice. We extend this framework and introduce the (2 + 1)-dimensional SCA, which can be interpreted as the ultradiscretization of the 2D Toda equation. We also construct the N-soliton solutions for this system.
All Science Journal Classification (ASJC) codes
- Statistical and Nonlinear Physics
- Mathematical Physics
- Physics and Astronomy(all)