Soliton solutions of a generalized discrete KdV equation
Masataka Kanki, Jun Mada, Tetsuji Tokihiro
TL;DR
This paper explores multi-soliton solutions of a generalized discrete KdV equation, revealing unique amplitude-dependent velocity behaviors and connecting them to the box ball system with a carrier.
Contribution
It introduces the analysis of soliton solutions in a generalized discrete KdV framework and explains unusual velocity-amplitude relationships via ultradiscrete limits.
Findings
Smaller amplitude solitons can move faster than larger ones.
The ultradiscrete limit relates the system to the box ball system with a carrier.
The behavior differs from classical KdV soliton solutions.
Abstract
We investigate the multi-soliton solutions to the generalized discrete KdV equation. In some cases a soliton with smaller amplitude moves faster than that with larger amplitude unlike the soliton solutions of the KdV equation. This phenomenon is intuitively understood from its ultradiscrete limit, where the system turns to the box ball system with a carrier. KEYWORDS: soliton, integrable equation, nonlinear system, discrete KdV equation, cellular automaton (v2: Final form to appear in J. Phys. Soc. Jpn.)
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.