Solitons and Particles in Cellular Automata: a Bibliography


Thanks to Professor Pawel Siwak, Poznan University of Technology, Poznan, Poland for providing many of these references. Please send me additions and corrections, thanks.

1986
J. K. Park, K. Steiglitz, and W. P. Thurston, ``Soliton-like behavior in automata,'' Physica D, vol. 19D, pp. 423-432, 1986. Reprinted in Theory and Applications of Cellular Automata, (S. Wolfram, ed.), World Scientific Publishing Co., Hong Kong (distributed by Taylor and Francis, Philadelphia), 1986, pp. 333-342.

1988
C. H. Goldberg, ``Parity filter automata,'' Complex Systems, vol. 2, pp. 91-141, 1988.

T. S. Papatheodorou, M. J. Ablowitz, and Y. G. Saridakis, ``A rule for fast computation and analysis of soliton automata,'' Studies in Applied Mathematics, vol. 79, pp. 173-184, 1988.

1989
A. S. Fokas, E. P. Papadopoulou, and Y. G. Saridakis, ``Particles in soliton cellular automata,'' Complex Systems, vol. 3, pp. 615-633, 1989.

A. S. Fokas, E. P. Papadopoulou, Y. G. Saridakis, and M. J. Ablowitz, ``Interaction of simple particles in soliton cellular automata,'' Studies in Applied Mathematics, vol. 81, pp. 153-180, 1989.

T. S. Papatheodorou, and A. S. Fokas, ``Evolution theory, periodic particles and solitons in cellular automata,'' Studies in Applied Mathematics, vol. 80, pp. 165-182, 1989.

T. S. Papatheodorou and N. B. Tsantanis, ``Fast soliton automata,'' pp. 41-47 in Optimal algorithms, H. Djidjev (ed.), LNCS 401, Springer-Verlag, Berlin 1989.

1990
M. J. Ablowitz, ``Nonlinear evolution equations, inverse scattering and cellular automata,'' pp. 1-26 in Solitons on Physics, Mathematics and Nonlinear Optics, P. J. Olver and D. H. Sattinger (eds.), Springer-Verlag, New York, 1990.

A. S. Fokas, ``New manifestations of solitons,'' pp. 65-77 in Solitons in Physics, Mathematics and Nonlinear Optics, P. J. Olver and D. H. Sattinger (eds.), Springer-Verlag, New York, 1990.

A. S. Fokas, E. P. Papadopoulou, and Y. G. Saridakis, ``Soliton cellular automata,'' Physica D, vol. 41, pp. 297-321, 1990.

A. S. Fokas, E. P. Papadopoulou, and Y. G. Saridakis, ``Coherent structures in cellular automata,'' Physics Letters A, vol. 147, no. 7, pp. 369-379, July 23, 1990.

D. Takahashi and J. Satsuma, ``A soliton cellular automaton,'' Journal of the Physical Society of Japan, vol. 59, no. 10, pp. 3514-3519, Oct. 1990.

1991
M. J. Ablowitz, J. M. Keiser and L. A. Takhtajan, ``A class of stable multistate time-reversible cellular automata with rich particle content,'' Physical Review A, vol. 44, no. 10, pp. 6909-6912, Nov. 15, 1991.

B. Fuchssteiner, ``Filter automata admitting oscillating carrier waves,'' Applied Mathematics Letters, vol.4, No. 6, pp. 23-26, 1991.

1992
M. Bruschi, P. M. Santini and O. Ragnisco, ``Integrable cellular automata,'' Physics Letters A, vol. 169, pp. 151-160, 1992.

Z. Jiang, ``An energy-conserved solitonic cellular automaton'', Journal of Physics A - Mathematical and General, vol. 25, No.11, pp. 3369-3381, 1992.

P. Siwak, ``Particles of parity-rule recursive filtering constructed by means of particle edge automata,'' KARiI, TR< 1.92, pp. 1-30, Jan. 1992.

1993
A. Bobenko, M. Bordeman, C. Gunn and U. Pinkall, ``On 2-integrable cellular automata,'' Communications in Mathematical Physics, vol. 158, no. 1, pp. 127-134, 1993.

P. Siwak, ``Introduction to filter automata theory,'' Studia z Automatyki, vol. 18, pp. 87-110, 1993.

1994
M. Bruschi and P. M. Santini, ``Cellular Automata in 1+1, 2+1 and 3+1 dimensions, constants of motion and coherent structures,'' Physica D, vol. 70, pp. 185-209, 1994.

P. Siwak, ``Models of filter automata,'' (in Polish), studia z Informatyki i Automatyki, vol. 19, pp. 77-97, 1994.

1995
T. Puchalka and P. Siwak, ``Automata and languages,'' Proceedings of the Second International Symposium on Methods and Models in Automation and Robotics (MMAR'95), 30 August - 2 September 1995, Midzyzdroje, Poland. S. Baka, S. Domek, Z. Emirsajow (eds.), Wyd. Uczelniane Politechniki Szczeciskiej, pp. 467-480, 1995.

P. Siwak, ``Filter automata and PRR fiiltering,'' Journal of Technical Physics, vol. 36, no. 1, pp. 153-163, 1995.

D. Takahashi and J. Matsukidaira, ``On discrete soliton equations related to cellular automata,'' Physics Letters A, vol. 209, pp. 184-188, 1995.

1996
T. Tohikiro, D. Takahashi, J. Matsukidaira and J. Satsuma, ``From Soliton Equations to Integrable Cellular Automata through a Limiting Procedure,'' Physical Review Letters, vol. 76, No. 18, pp. 3247-3250, April 29, 1996

M. Torii, D. Takahashi and J. Satsuma, ``Combinatorial representation of invariants of a soliton cellular automaton,'' Physica D, vol. 92, No. 3-4, pp. 209-220, 1996.

1997
B. Grammaticos, Y. Ohta, A. Ramani, D. Takahashi and K. M. Tamizhmani, ``Cellular automata and ultra-discrete Painleve equations,'' Physics Letters A, vol. 226, pp. 53-58, Feb. 10, 1997.

J. Matsukidaira, J. Satsuma, D. Takahashi, T. Tokihiro and M. Torii, ``Toda-type cellular automaton and its N-soliton solution,'' Physics Letters A, vol. 225, pp. 287-295, 1997.

A. Nagai, T. Tokihiro, J. Satsuma, R. Willox and K. Kajiwara, ``Two-dimensional soliton cellular automaton of deautonomized Toda-type,'' Physics Letters A, vol. 234, Iss. 4, pp. 301-309, Oct. 6, 1997.

1998
A. K. Pogrebkov, ``Discrete Schrodinger equation on finite field and associated cellular automaton,'' xyz: math-ph/9811007, pp. 1-13, Nov. 10, 1998.

P. Siwak, ``Filtrons and their associated ring computations,'' International Journal of General Systems, (Special Issue on General Physical Systems and the Emergence of Physical Structure from Information Theory), vol. 27, issue 1-3, pp. 181-229, 1998

P. Siwak, ``On automata of some discrete recursive filters that support the filtrons,'' Proceedings of the Fifth International Symposium on Methods and Models in Automation and Robotics (MMAR'98), August 25-29, 1998, Miedzyzdroje, Poland, S. Domek, R. Kaszynski, L. Tarasiejski (eds.). Printed by Wydawnictwo Politechniki Szczecinskiej. Vol. 3 (Discrete Processes), pp. 1069-1074, 1998.

P. Siwak, ``Iterons, fractals and computations of automata,'' to appear in the American Institute of Physics (AIP) Conference Proceedings, The Second International Conference on Computing Anticipatory Systems, Liege, Belgium, August 10-14, 1998. An extended abstract in: CASYS'98 Abstract Book, published by CHAOS asbl, 1998, Daniel M. Dubois (ed.), pp. 18-20, Symposium 5, 1998.