articles
The ultradiscrete analogues with parity variables of the so-called hard spring equation and its conserved quantity are proposed. Solutions of the resulting equation are constructed for many initial values, and a diagram is proposed to illustrate the structure of each solution. The behavior of the solutions is classified into four (or precisely five) types, two of which are periodic. Then, the ultradiscrete analogue of the conserved quantity is investigated to determine whether the conserved quantity is preserved for each solution. Three types of behavior are observed for the “ultradiscretized conserved quantity,” which is actually preserved in one type but not always in the other types. However, perfect matching between the behavior of the ultradiscrete solutions and that of the ultradiscretized conserved quantity is observed, and the mathematical structure partly survives through ultradiscretization.
Ultradiscrete analogues of the hard-spring equation and its conserved quantity
http://link.springer.com/10.1007/s13160-018-0329-5
2019-04-10T19:56
en
2019-01
research_article
false
1-26
2019-01-01
https://scigraph.springernature.com/explorer/license/
readcube_id
02a0b8b1405463fd20ab9d0acbe346bfae5ccc56bbf3fc0f70975dbc6e349c72
Hirotaka
Toyama
10.1007/s13160-018-0329-5
doi
Mathematical Sciences
pub.1106706039
dimensions_id
Shin
Isojima
1868-937X
0916-7005
Japan Journal of Industrial and Applied Mathematics
Pure Mathematics
Department of Industrial and Systems Engineering, Faculty of Science and Engineering, Hosei University, 3-7-2, Kajino-cho, 184-8584, Koganei-shi, Tokyo, Japan
Hosei University
Springer Nature - SN SciGraph project