Schrödinger Equation with Convolution Nonlinearity on Lie Groups and Commutative Homogeneous Spaces

A. I. Breev

    Research output: Contribution to journal › Article

    1 Citation (Scopus)

    Abstract

    The Schrödinger equation with nonlocal nonlinearity of convolution type on Lie groups and commutative homogeneous spaces is considered. It is shown that in the special case of an abelian group the Schrödinger equation admits a solution in the form of a superposition of non-interacting solitons. In the case of a commutative homogeneous space, a noncommutative reduction of the Schrödinger equation is carried out. A general solution in the particular case when the nonlinearity factorizes in the spatial variables is found.

    Original languageEnglish
    Pages (from-to)1050-1058
    Number of pages9
    JournalRussian Physics Journal
    Volume57
    Issue number8
    DOIs
    Publication statusPublished - Dec 2014

    Fingerprint

    convolution integrals
    nonlinearity
    solitary waves

    Keywords

    • method of orbits
    • Schrödinger equation with convolution nonlinearity
    • λ-representation

    ASJC Scopus subject areas

    • Physics and Astronomy(all)

    Cite this

    Schrödinger Equation with Convolution Nonlinearity on Lie Groups and Commutative Homogeneous Spaces. / Breev, A. I.

    In: Russian Physics Journal, Vol. 57, No. 8, 12.2014, p. 1050-1058.

    Research output: Contribution to journal › Article

    Breev, AI 2014, 'Schrödinger Equation with Convolution Nonlinearity on Lie Groups and Commutative Homogeneous Spaces', Russian Physics Journal, vol. 57, no. 8, pp. 1050-1058. https://doi.org/10.1007/s11182-014-0343-2
    Breev AI. Schrödinger Equation with Convolution Nonlinearity on Lie Groups and Commutative Homogeneous Spaces. Russian Physics Journal. 2014 Dec;57(8):1050-1058. https://doi.org/10.1007/s11182-014-0343-2
    Breev, A. I. / Schrödinger Equation with Convolution Nonlinearity on Lie Groups and Commutative Homogeneous Spaces. In: Russian Physics Journal. 2014 ; Vol. 57, No. 8. pp. 1050-1058.
    @article{1cc4cfd125d4441d92d2f729604bd9dd,
    title = "Schr{\"o}dinger Equation with Convolution Nonlinearity on Lie Groups and Commutative Homogeneous Spaces",
    abstract = "The Schr{\"o}dinger equation with nonlocal nonlinearity of convolution type on Lie groups and commutative homogeneous spaces is considered. It is shown that in the special case of an abelian group the Schr{\"o}dinger equation admits a solution in the form of a superposition of non-interacting solitons. In the case of a commutative homogeneous space, a noncommutative reduction of the Schr{\"o}dinger equation is carried out. A general solution in the particular case when the nonlinearity factorizes in the spatial variables is found.",
    keywords = "method of orbits, Schr{\"o}dinger equation with convolution nonlinearity, λ-representation",
    author = "Breev, {A. I.}",
    year = "2014",
    month = "12",
    doi = "10.1007/s11182-014-0343-2",
    language = "English",
    volume = "57",
    pages = "1050--1058",
    journal = "Russian Physics Journal",
    issn = "1064-8887",
    publisher = "Consultants Bureau",
    number = "8",

    }

    TY - JOUR

    T1 - Schrödinger Equation with Convolution Nonlinearity on Lie Groups and Commutative Homogeneous Spaces

    AU - Breev, A. I.

    PY - 2014/12

    Y1 - 2014/12

    N2 - The Schrödinger equation with nonlocal nonlinearity of convolution type on Lie groups and commutative homogeneous spaces is considered. It is shown that in the special case of an abelian group the Schrödinger equation admits a solution in the form of a superposition of non-interacting solitons. In the case of a commutative homogeneous space, a noncommutative reduction of the Schrödinger equation is carried out. A general solution in the particular case when the nonlinearity factorizes in the spatial variables is found.

    AB - The Schrödinger equation with nonlocal nonlinearity of convolution type on Lie groups and commutative homogeneous spaces is considered. It is shown that in the special case of an abelian group the Schrödinger equation admits a solution in the form of a superposition of non-interacting solitons. In the case of a commutative homogeneous space, a noncommutative reduction of the Schrödinger equation is carried out. A general solution in the particular case when the nonlinearity factorizes in the spatial variables is found.

    KW - method of orbits

    KW - Schrödinger equation with convolution nonlinearity

    KW - λ-representation

    UR - http://www.scopus.com/inward/record.url?scp=84925487344&partnerID=8YFLogxK

    UR - http://www.scopus.com/inward/citedby.url?scp=84925487344&partnerID=8YFLogxK

    U2 - 10.1007/s11182-014-0343-2

    DO - 10.1007/s11182-014-0343-2

    M3 - Article

    VL - 57

    SP - 1050

    EP - 1058

    JO - Russian Physics Journal

    JF - Russian Physics Journal

    SN - 1064-8887

    IS - 8

    ER -

    Access to Document