Oceanic Dissipative Nonlinear Schr¨odinger Equation for Deep and Shallow Water Interactions: Bohmian Hydrodynamics, Ermakov–Lewis Invariant, Solitons and Feynman Propagator

Daniel Gemaque Gemaque da Silva

Published Jan 1, 2026• 0 citations

Abstract

We propose a dissipative nonlinear Schr¨odinger equation describing interactions between deep and shallow oceanic waves within the de Broglie–Bohm hydrodynamic formalism. The model incorporates logarithmic, cubic and square-root nonlinearities without the presence of a harmonic oscillator potential. Through a suitable transformation, the dissipative continuity equation and dissipative Euler equation are mapped into conservative forms. The corresponding Ermakov–Lewis invariant is obtained, together with hybrid solitonic solutions and the associated Feynman propagator. The uncertainty relation is analyzed in terms of the competition between logarithmic confinement and nonlinear oceanic interactions.

DOI: 10.17605/osf.io/g8pz2

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