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Rational interpolation to solutions of Riccati difference equations on elliptic lattices

✍ Scribed by Alphonse P. Magnus

Book ID
104006665
Publisher
Elsevier Science
Year
2009
Tongue
English
Weight
747 KB
Volume
233
Category
Article
ISSN
0377-0427

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✦ Synopsis

It is shown how to define difference equations on particular lattices {x n }, n ∈ Z, where the x n s are values of an elliptic function at a sequence of arguments in arithmetic progression (elliptic lattice). Solutions to special difference equations (elliptic Riccati equations) have remarkable simple (!) interpolatory continued fraction expansions.

πŸ“œ SIMILAR VOLUMES

Symbolic computation of Jacobi elliptic
Symbolic computation of Jacobi elliptic function solutions to nonlinear differential-difference equations
✍ Xuelin Yong; Xin Zeng; Zhiyong Zhang; Yufu Chen πŸ“‚ Article πŸ“… 2009 πŸ› Elsevier Science 🌐 English βš– 481 KB

In this paper, an algorithm is presented to find exact polynomial solutions of nonlinear differential-difference equations(DDEs) in terms of the Jacobi elliptic functions. The key steps of the algorithm are illustrated by the discretized mKdV lattice. A Maple package JACOBI is developed based on the