Ultradiscrete Permanent Solution to the Ultradiscrete KP Equation
Hidetomo Nagai
TL;DR
This paper introduces an ultradiscrete permanent as a novel solution to the ultradiscrete KP equation, expanding the mathematical tools available for ultradiscrete integrable systems.
Contribution
It presents the ultradiscrete permanent as a new solution method for the ultradiscrete KP equation, including explicit examples and additional relations beyond the dispersion relation.
Findings
The ultradiscrete permanent satisfies the ultradiscrete KP equation.
Explicit examples of ultradiscrete permanent solutions are provided.
Additional relations are identified that are necessary for the solution.
Abstract
We propose an ultradiscrete permanent solution to the ultradiscrete KP equation. The ultradiscrete permanent is an ultradiscrete analogue of the usual permanent. The elements on this ultradiscrete permanent solution are required some additional relations other than the ultradiscrete dispersion relation. We confirm the solution satisfying these relations and propose some explicit examples of the solution.
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.
Taxonomy
TopicsNonlinear Waves and Solitons · Advanced Mathematical Physics Problems · Nonlinear Photonic Systems