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

Abstract

An overview is presented of quantum and resonant nonlinear Schro<spacing diaeresis>dinger 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-Painleve II and associated Painleve XXXIV integrable similarity reductions are derived.