The short pulse equation and associated constraints
Theodoros P. Horikis
TL;DR
This paper investigates the short pulse equation (SPE) as an initial-boundary value problem, revealing integral constraints necessary for solution regularity and showing how these constraints evolve dynamically.
Contribution
It introduces the concept of integral constraints for SPE solutions and demonstrates their dynamic generation through the evolution equation.
Findings
Solutions must satisfy integral relations for regularity
An infinite number of constraints can be generated dynamically
Discontinuities in the temporal derivative are linked to constraint violations
Abstract
The short pulse equation (SPE) is considered as an initial-boundary value problem. It is found that the solutions of the SPE must satisfy an integral relation otherwise the temporal derivative exhibits discontinuities. This integral relation is not necessary for a solution to exist. An infinite number of such constraints can be dynamically generated by the evolution equation.
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.