A Stochastic Model for Solitons

Yoshiaki Itoh, Hosam M. Mahmoud, Daisuke Takahashi

    Research output: Contribution to journalArticle

    1 Citation (Scopus)

    Abstract

    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].

    Original languageEnglish
    Pages (from-to)51-64
    Number of pages14
    JournalRandom Structures and Algorithms
    Volume24
    Issue number1
    DOIs
    Publication statusPublished - 2004 Jan

    Fingerprint

    Stochastic models
    Solitons
    Stochastic Model
    Stationary Distribution
    Wavelength
    Gumbel Distribution
    Steady-state Distribution
    Cellular automata
    Limit Distribution
    Deterministic Model
    Convolution
    Random variables
    Japan
    Cellular Automata
    Wave propagation
    Probability distributions
    Jump
    Probability Distribution
    Physics
    Aging of materials

    Keywords

    • Limit distribution
    • Random structure
    • Soliton
    • Wave propagation

    ASJC Scopus subject areas

    • Computer Graphics and Computer-Aided Design
    • Software
    • Mathematics(all)
    • Applied Mathematics

    Cite this

    A Stochastic Model for Solitons. / Itoh, Yoshiaki; Mahmoud, Hosam M.; Takahashi, Daisuke.

    In: Random Structures and Algorithms, Vol. 24, No. 1, 01.2004, p. 51-64.

    Research output: Contribution to journalArticle

    Itoh, Yoshiaki ; Mahmoud, Hosam M. ; Takahashi, Daisuke. / A Stochastic Model for Solitons. In: Random Structures and Algorithms. 2004 ; Vol. 24, No. 1. pp. 51-64.
    @article{dee4fbb35bc443219cb16e8f35d21831,
    title = "A Stochastic Model for Solitons",
    abstract = "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].",
    keywords = "Limit distribution, Random structure, Soliton, Wave propagation",
    author = "Yoshiaki Itoh and Mahmoud, {Hosam M.} and Daisuke Takahashi",
    year = "2004",
    month = "1",
    doi = "10.1002/rsa.10106",
    language = "English",
    volume = "24",
    pages = "51--64",
    journal = "Random Structures and Algorithms",
    issn = "1042-9832",
    publisher = "John Wiley and Sons Ltd",
    number = "1",

    }

    TY - JOUR

    T1 - A Stochastic Model for Solitons

    AU - Itoh, Yoshiaki

    AU - Mahmoud, Hosam M.

    AU - Takahashi, Daisuke

    PY - 2004/1

    Y1 - 2004/1

    N2 - 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].

    AB - 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].

    KW - Limit distribution

    KW - Random structure

    KW - Soliton

    KW - Wave propagation

    UR - http://www.scopus.com/inward/record.url?scp=0348199034&partnerID=8YFLogxK

    UR - http://www.scopus.com/inward/citedby.url?scp=0348199034&partnerID=8YFLogxK

    U2 - 10.1002/rsa.10106

    DO - 10.1002/rsa.10106

    M3 - Article

    VL - 24

    SP - 51

    EP - 64

    JO - Random Structures and Algorithms

    JF - Random Structures and Algorithms

    SN - 1042-9832

    IS - 1

    ER -