ON ASYMPTOTIC BEHAVIOR OF SOLUTIONS TO CUBIC NONLINEAR KLEIN-GORDON SYSTEMS IN ONE SPACE DIMENSION

Satoshi Masaki, Jun Ichi Segata, Kota Uriya

    研究成果: ジャーナルへの寄稿学術誌査読

    3 被引用数 (Scopus)

    抄録

    In this paper, we consider the large time asymptotic behavior of solutions to systems of two cubic nonlinear Klein-Gordon equations in one space dimension. We classify the systems by studying the quotient set of a suitable subset of systems by the equivalence relation naturally induced by the linear transformation of the unknowns. It is revealed that the equivalence relation is well described by an identification with a matrix. In particular, we characterize some known systems in terms of the matrix and specify all systems equivalent to them. An explicit reduction procedure from a given system in the suitable subset to a model system, i.e., to a representative, is also established. The classification also draws our attention to some model systems which admit solutions with a new kind of asymptotic behavior. Especially, we find new systems which admit a solution of which decay rate is worse than that of a solution to the linear Klein-Gordon equation by logarithmic order.

    本文言語英語
    ページ(範囲)517-563
    ページ数47
    ジャーナルTransactions of the American Mathematical Society Series B
    9
    DOI
    出版ステータス出版済み - 2022

    !!!All Science Journal Classification (ASJC) codes

    • 数学(その他)

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