Real-Spectrum Darboux Limits at Multiple Spatial Roots of the Coupled Fokas-Lenells System

Muchen Dong; Lei Wang

Real-Spectrum Darboux Limits at Multiple Spatial Roots of the Coupled Fokas-Lenells System

Exactly Solvable and Integrable Systems 2026-07-20 v1

Authors: Muchen Dong , Lei Wang

Abstract

We investigate Darboux constructions generated by multiple spatial roots of the coupled Fokas-Lenells system on a plane-wave background. Nonreal double roots give regular one-fold transformations, whereas real double and triple roots require directional real-spectrum limits. We classify the admissible projective null sets, derive the leading spectral corrections, and establish global regularity. A critical background relation additionally produces a persistent zero branch, leading to distinct nonlocal plateaus along parabolic corridors, cubic level sets, and a characteristic line.

Keywords

Fokas-Lenells system Darboux transformations multiple spatial roots real-spectrum limits plane-wave background global regularity

Cite

@article{arxiv.2607.17955,
  title  = {Real-Spectrum Darboux Limits at Multiple Spatial Roots of the Coupled Fokas-Lenells System},
  author = {Muchen Dong and Lei Wang},
  journal= {arXiv preprint arXiv:2607.17955},
  year   = {2026}
}