Whitham-Broer-Kaup Systems in Multi-dimensions: Quantum and Resonant NLS Connections
Exactly Solvable and Integrable Systems
2025-08-04 v1
Abstract
An overview is presented of quantum and resonant nonlinear Schr\"odinger equation links to Whitham-Broer-Kaup type systems. A novel n+1-dimensional extension of the Whitham-Broer-Kaup hydrodynamic system is constructed with connection to an equivalent multi-dimensional resonant NLS equation. Hybrid Ermakov-Painlev\'e II and associated Painlev\'e XXXIV integrable similarity reductions are derived.
Keywords
Cite
@article{arxiv.2508.00660,
title = {Whitham-Broer-Kaup Systems in Multi-dimensions: Quantum and Resonant NLS Connections},
author = {Oktay K Pashaev and Colin Rogers},
journal= {arXiv preprint arXiv:2508.00660},
year = {2025}
}
Comments
30 pages