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Soliton Distribution in the Ball and Box Cellular Automation Model
American Journal of Mathematical and Computer Modelling
Volume 4, Issue 1, March 2019, Pages: 27-30
Received: Apr. 3, 2019; Accepted: May 16, 2019; Published: Jun. 13, 2019
Authors
Alpha Soko, Department of Mathematics, Mzuzu University, Mzuzu, Malawi
James Makungu, Department of Mathematics, University of Dar es Salaam, Dar es Salaam, Tanzania
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Abstract
Solitons are very important waves in Mathematical Physics. They help model many physical situations for instance tsunami waves, application in optical communication systems, application in plasma physics and application in laser guided technology among others. Despite enormous applications, solving the non-linear equations which have soliton solutions is challenging be- cause the nonlinear characteristic of the system abruptly changes due to some slight changes of valid parameters including time. A remedy to this is to use cellular automation models to model soliton dynamics. Cellular automation models do not change in response to slight changes on parameters. In this paper, using computer simulation, an investigation of the distribution of the number of solitons from the Ball and Box cellular automation model was examined. The distribution of the number of solitons from the two and three colour Ball and Box cellular automation was established. Using the online integer sequence, for the two colour Ball and Box cellular automation model, it was found that the distribution of the number of the solitons is indexed by the binomial coefficients. On the Other hand, for the three colour Ball and Box cellular automation model, it was found that only solitons of lengths one to four possesses the distribution while the other soliton lengths do not possess any distribution function.
Keywords
Solitons, Ball and Box Model, Cellular Automation, Integer Sequence, Binomial Coefficients
Alpha Soko, James Makungu, Soliton Distribution in the Ball and Box Cellular Automation Model, American Journal of Mathematical and Computer Modelling. Vol. 4, No. 1, 2019, pp. 27-30. doi: 10.11648/j.ajmcm.20190401.14
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