Lotka-Volterra Equation over a Finite Ring Z/p^N Z

Abstract

Discrete Lotka-Volterra equation over $p$-adic space was constructed since $p$-adic space is a prototype of spaces with the non-Archimedean valuations and the space given by taking ultra-discrete limit studied in soliton theory should be regarded as a space with the non-Archimedean valuations in the previous report (solv-int/9906011). In this article, using the natural projection from $p$-adic integer to a ring $Z/p^{n}Z$, a soliton equation is defined over the ring. Numerical computations shows that it behaves regularly.

LaTex, 10 pages

References in corpus (1)

• p-adic Difference-Difference Lotka-Volterra Equation and Ultra-Discrete Limit

Cited by in corpus (1)

• Toda Equations and $\sigma$-Functions of Genera One and Two