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Ultradiscretization with parity variables (pUD) is a method of constructing a conditional piecewise linear equation which approximates a given difference equation. Its application is not limited to subtraction-free equation, being… Click to show full abstract
Ultradiscretization with parity variables (pUD) is a method of constructing a conditional piecewise linear equation which approximates a given difference equation. Its application is not limited to subtraction-free equation, being different from the traditional ultradiscretization. In this paper, the procedure of pUD is applied to the van der Pol equation, which is a non-integrable system, and it is studied how the procedure works. The behavior of the ultradiscrete solution is understood by summarizing in transition diagrams, and some periodic solutions are found.
Journal Title: Nonlinearity
Year Published: 2022
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