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.
ASJC Scopus subject areas
- Statistical and Nonlinear Physics
- Mathematical Physics
- General Physics and Astronomy