On asymptotic behavior of solutions to cubic nonlinear Klein-Gordon systems in one space dimension
On asymptotic behavior of solutions to cubic nonlinear Klein-Gordon systems in one space dimension
复制标题
一维三次非线性克莱因-戈登系统解的渐近行为
DOI：
10.1090/btran/116
复制
发表时间：
2022
期刊：
影响因子：
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通讯作者：
Uriya Kota
中科院分区：
文献类型：
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作者：
Masaki Satoshi;Segata Jun-ichi;Uriya Kota
本文考虑一维空间中两个三次非线性Klein-Gordon方程组解的大时间渐近性态。我们通过研究系统的一个合适的子集的商集的等价关系自然诱导的未知数的线性变换的系统进行分类。它揭示了等价关系是很好地描述了一个矩阵的标识。特别是，我们描述了一些已知的系统中的矩阵，并指定所有系统与他们等价。建立了从合适子集中的给定系统到模型系统，即到代表系统的显式约化过程。分类也提请我们注意一些模型系统，承认一种新的渐近行为的解决方案。特别是，我们发现新的系统，承认的解决方案，其衰减率比对数阶的线性Klein-Gordon方程的解决方案更差。引用
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, ie, 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. References