Ultradiscretization of elliptic functions and its applications to integrable systems

Atsushi Nobe

doi:10.1088/0305-4470/39/20/L07

Ultradiscretization of elliptic functions and its applications to integrable systems

Atsushi Nobe^*

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

5 Citations (Scopus)

Abstract

It is shown that there exist three kinds of ultradiscrete analogues of Jacobi's elliptic functions. In this process, the asymptotic behaviour of the poles and the zeros of the functions plays a crucial role. Using the ultradiscrete analogues and an addition formula, exact solutions to the ultradiscrete KP equation are constructed, and their relation to the ultradiscrete QRT system is discussed.

Original language	English
Pages (from-to)	L335-L342
Journal	Journal of Physics A: Mathematical and General
Volume	39
Issue number	20
DOIs	https://doi.org/10.1088/0305-4470/39/20/L07
Publication status	Published - 2006 May 19
Externally published	Yes

ASJC Scopus subject areas

Statistical and Nonlinear Physics
Mathematical Physics
Physics and Astronomy(all)

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10.1088/0305-4470/39/20/L07

Cite this

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abstract = "It is shown that there exist three kinds of ultradiscrete analogues of Jacobi's elliptic functions. In this process, the asymptotic behaviour of the poles and the zeros of the functions plays a crucial role. Using the ultradiscrete analogues and an addition formula, exact solutions to the ultradiscrete KP equation are constructed, and their relation to the ultradiscrete QRT system is discussed.",

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AB - It is shown that there exist three kinds of ultradiscrete analogues of Jacobi's elliptic functions. In this process, the asymptotic behaviour of the poles and the zeros of the functions plays a crucial role. Using the ultradiscrete analogues and an addition formula, exact solutions to the ultradiscrete KP equation are constructed, and their relation to the ultradiscrete QRT system is discussed.

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Ultradiscretization of elliptic functions and its applications to integrable systems

Abstract

ASJC Scopus subject areas

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