Establishment of ultradiscretization with parity variables and its application to integrable systems

2017 Fiscal Year Final Research Report

• Project/Area Number: 26790082
• Research Category: Grant-in-Aid for Young Scientists (B)
• Allocation Type: Multi-year Fund
• Research Field: Computational science
• Research Institution: Hosei University
• Principal Investigator: ISOJIMA Shin 法政大学, 理工学部, 准教授 (90422394)
• Project Period (FY): 2014-04-01 – 2018-03-31
• Keywords: 超離散化 / 可積分系 / パンルヴェ方程式 / 戸田格子方程式 / カルマンフィルタ / 交通流モデル

Outline of Final Research Achievements

In this research, many results on the method of ultradiscretization with parity variables (p-UD) were obtained, such as, oscillatory solutions of the p-UD Toda equation, a class of special solutions of the p-UD Painleve II and III equations, proposal of ultradiscrete Kalman filtering and its validation, p-UD of the nonlinear spring equation and its preserving quantity, ultradiscrete traffic-flow models. New examples of p-UD were proposed, and validity of the method was discussed. Some technical notes of the method are also recognized through these studies.
On the other hand, it is not sufficient to extend these results to a general theory (for example, ultradiscretization of the determinants), and to give back to continuous systems. Additional research is required to resolve these questions.

Free Research Field

非線形可積分系