Hodograph solutions of the dispersionless coupled KdV hierarchies, critical points and the Euler-Poisson-Darboux equation
B. Konopelchenko, L. Martinez Alonso, E. Medina
TL;DR
This paper explores how hodograph solutions of dispersionless coupled KdV hierarchies relate to critical points of a function satisfying the Euler-Poisson-Darboux equation, revealing connections to singular sectors and shock singularities.
Contribution
It establishes a link between hodograph solutions of dcKdV hierarchies and critical points of an Euler-Poisson-Darboux function, including higher genus hierarchies and shock solutions.
Findings
Hodograph solutions correspond to critical points of a scalar function.
Singular sectors are described by higher genus dcKdV hierarchies.
Concrete shock-type solutions are constructed.
Abstract
It is shown that the hodograph solutions of the dispersionless coupled KdV (dcKdV) hierarchies describe critical and degenerate critical points of a scalar function which obeys the Euler-Poisson-Darboux equation. Singular sectors of each dcKdV hierarchy are found to be described by solutions of higher genus dcKdV hierarchies. Concrete solutions exhibiting shock type singularities are presented.
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.