Solitons with Nested Structure over Finite Fields(Theory)

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  • YURA Fumitaka
    Department of Complex and Intelligent Systems Future University HAKODATE

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  • 有限体上のソリトン方程式における入れ子構造を持つソリトン解について(理論)
  • 有限体上のソリトン方程式における入れ子構造を持つソリトン解について
  • ユウゲンタイ ジョウ ノ ソリトン ホウテイシキ ニ オケル イレコ コウゾウ オ モツ ソリトンカイ ニ ツイテ

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Abstract

In this paper, we prove the one-soliton solutions to the solitonic dynamical system over finite fields that may be regarded as an analogue of the box-ball systems. It turns out that the one-soliton solution has a nested structure similar to fractals, and as far as we know such a system seems to be novel. Furthermore, in spite of such a complex internal structure, numerical simulations show stable propagations before and after collisions among multiple solitons with preserving their patterns.

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