Rei Inoue and Kazuhiro Hikami 1999 J. Phys. A: Math. Gen. 32 6853 doi:10.1088/0305-4470/32/39/310
Construction of soliton cellular automaton from the vertex model - the discrete 2D Toda equation and the Bogoyavlensky lattice
Rei Inoue and Kazuhiro Hikami
Show affiliationsWe 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.
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Issue 39 (1 October 1999)
Received 26 May 1999, in final form 27 July 1999
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Construction of soliton cellular automaton from the vertex model - the discrete 2D Toda equation and the Bogoyavlensky lattice
Rei Inoue and Kazuhiro Hikami 1999 J. Phys. A: Math. Gen. 32 6853
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