A Stochastic Model for Solitons

Yoshiaki Itoh, Hosam M. Mahmoud*, Daisuke Takahashi


研究成果: Article査読

4 被引用数 (Scopus)


The soliton physics for the propagation of waves is represented by a stochastic model in which the particles of the wave can jump ahead according to some probability distribution. We demonstrate the presence of a steady state (stationary distribution) for the wavelength. It is shown that the stationary distribution is a convolution of geometric random variables. Approximations to the stationary distribution are investigated for a large number of particles. The model is rich and includes Gaussian cases as limit distribution for the wavelength (when suitably normalized). A sufficient Lindeberg-like condition identifies a class of solitons with normal behavior. Our general model includes, among many other reasonable alternatives, an exponential aging soliton, of which the uniform soliton is one special subcase (with Gumbel's stationary distribution). With the proper interpretation, our model also includes the deterministic model proposed in Takahashi and Satsuma [A soliton cellular automaton, J Phys Soc Japan 59 (1990), 3514-3519].

ジャーナルRandom Structures and Algorithms
出版ステータスPublished - 2004 1月

ASJC Scopus subject areas

  • ソフトウェア
  • 数学 (全般)
  • コンピュータ グラフィックスおよびコンピュータ支援設計
  • 応用数学


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