A Novel Geometric Realization of the Yajima-Oikawa Equations
Differential Geometry
2024-12-18 v1 Exactly Solvable and Integrable Systems
Abstract
We show that the Yajima-Oikawa (YO) equations, a model of short wave-long wave interaction, arise from a simple geometric flow on curves in the 3-dimensional sphere that are transverse to the standard contact structure. For the family of periodic plane wave solutions of the YO equations studied by Wright, we construct the associated transverse curves, derive their closure condition, and exhibit several examples with non-trivial topology.
Keywords
Cite
@article{arxiv.2412.12946,
title = {A Novel Geometric Realization of the Yajima-Oikawa Equations},
author = {Annalisa Calini and Thomas A. Ivey},
journal= {arXiv preprint arXiv:2412.12946},
year = {2024}
}
Comments
13 pages, 4 figures