Solutions to the ultradiscrete KdV equation expressed as the maximum of a quadratic function
arXiv:1302.1927 · doi:10.1088/1751-8113/46/26/265203
Abstract
We propose the functions defined by the maximum of a discrete quadratic form and satisfying the ultradiscrete KdV equation. These functions includes not only soliton solutions but also pseudo-periodic solutions. In the proof, we employ some facts of discrete convex analysis.
16 pages, 4 figures