English

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 S3S^3 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