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

Satoshi Masaki, Jun Ichi Segata, Kota Uriya

    Research output: Contribution to journalArticlepeer-review

    3 Citations (Scopus)

    Abstract

    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.

    Original languageEnglish
    Pages (from-to)517-563
    Number of pages47
    JournalTransactions of the American Mathematical Society Series B
    Volume9
    DOIs
    Publication statusPublished - 2022

    All Science Journal Classification (ASJC) codes

    • Mathematics (miscellaneous)

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