Ultradiscrete hard-spring equation and its phase plane analysis
Ultradiscrete hard-spring equation and its phase plane analysis
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超离散硬弹簧方程及其相平面分析
DOI：
10.1007/s13160-023-00568-9
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发表时间：
2023
影响因子：
0.9
通讯作者：
Suzuki Seiichiro
中科院分区：
文献类型：
--
作者：
Isojima Shin;Suzuki Seiichiro
超离散化使我们能够构造一个分段线性方程，它近似于一个给定的减自由差分方程。最近提出的“奇偶变量超离散化”（pUD）可以用减法处理方程。然而，在某些特定条件下，它的解可能有无限多个分支。本文研究了硬弹簧方程的pUD解。将pUD方程重新解释为相平面上一个集合到另一个集合的映射，并通过近似转移图分析解的行为，从而将无限分支转化为几个有限分支，使理解更容易。
Ultradiscretization enables us to construct a piecewise linear equation which approximates a given subtraction-free difference equation. Recently proposed “ultradiscretization with parity variables” (pUD) can treat an equation with subtraction. However, its solution may have an infinite number of branches under some specific conditions. In this paper, solutions of pUD for the hard-spring equation is investigated. The pUD equation is reinterpreted as the mapping which maps a set on the phase plane to another one, and the behaviour of the solutions are analyzed through approximative transition diagrams.As a result, the infinite branches are translated into a few finite branches and allowed easier understanding.