Whitham-Broer-Kaup Systems in Multi-dimensions: Quantum and Resonant NLS Connections

2025/08/01 by Pashaev, Oktay K, Rogers, Colin
#Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Physical sciences

paper · doi:10.48550/arxiv.2508.00660

Abstract

An overview is presented of quantum and resonant nonlinear Schrödinger 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-Painlevé II and associated Painlevé XXXIV integrable similarity reductions are derived.

Citations

• A Novel Ermakov–Painlevé II System: ‐Dimensional Coupled NLS and Elastodynamic Reductions
• Ermakov–Ray–Reid Reductions of Variational Approximations in Nonlinear Optics
• On a 2+1‐Dimensional Whitham–Broer–Kaup System: A Resonant NLS Connection
• A Higher-Order Water-Wave Equation and the Method for Solving It

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