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

2025/08/01 by Oktay K Pashaev, Colin Rogers, Pashaev, Oktay K +1 · 1 voice
Physics and Astronomy · #Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Physical sciences #nlin.SI

paper · pdf · 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

Discussions

• Oktay K Pashaev, Colin Rogers: Whitham-Broer-Kaup Systems in Multi-dimensions: Quantum and Resonant NLS Connections https://arxiv.org/abs/2508.00660 https://arxiv.org/pdf/2508.00660 https://arxiv.org/ [bsky, 1 points, 0 comments]

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