Nonlinear Schr¨odinger Equation with Oceanic Structure: Bohmian Dynamics, Ermakov–Lewis Invariant and Feynman Propagator

Daniel Gemaque da Silva

Published May 8, 2026• 0 citations

Abstract

We develop a nonlinear Schr¨odinger equation with an oceanicinspired structure. Using the de Broglie–Bohm formalism with an adimensional phase, we derive the hydrodynamic equations, obtain Gaussian solutions with time-dependent width, construct an ErmakovLewis-type invariant, and present a Feynman propagator formulation.

DOI: 10.5281/zenodo.20077890

Related papers

Nonlinear Schr¨odinger Equation with Exponential Oceanic Growth and Logarithmic Dissipation: A Bohmian Hydrodynamic Approach with Ermakov–Lewis Structure

Daniel Gemaque da Silva

Wepropose a nonlinear dissipative Schr¨odinger equation describing deep oceanic wave envelopes with exponential growth, logarithmic dissipation, and Bohmian hydrodynamic structure. The model combines a logarithmic nonlinear interaction with a time-dependent Ermakov–Lewis framework, generating dissipative continuity and Euler equations in the Madelung–Bohm representation. The resulting formalism admits Gaussian envelope solutions, rogue-wave growth regimes, and dissipative soliton-like structures. An associated Ermakov equation governing the temporal width of the oceanic envelope is derived, together with a generalized ErmakovLewis invariant. The theory establishes a connection between nonlinear quantum hydrodynamics and oceanic wave dynamics in deep water environments.

May 9, 20260 citations

Nonlinear Bohmian Schr¨odinger Equation for Oceanic Waves with Saturable Curvature Effects, Ermakov–Lewis Invariant, Feynman Propagator and Solitonic Solutions

Daniel Gemaque da Silva

A nonlinear Bohmian Schr¨odinger equation for oceanic wave dynamics is proposed using the Madelung–de Broglie–Bohm hydrodynamic formalism. The probability density is interpreted as the oceanic wave intensity. The model incorporates saturable nonlinear effects, curvature corrections and nonlinear gradient contributions. The associated continuity equation and Euler-type equation are derived. A generalized Ermakov–Lewis invariant is developed together with a Bohmian Feynman propagator. Exact bright soliton solutions are obtained in the weak saturation regime. The model may describe coherent oceanic structures, rogue-wave precursors and nonlinear hydrodynamic wave packets.

May 11, 20260 citations

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

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.

Jan 1, 20260 citations

Nonlinear Schr¨odinger Equation with Oceanic Structure: A Bohmian Approach with Adimensional Phase

Daniel Gemaque da Silva

Wepropose a nonlinear Schr¨odinger equation with an oceanic-type nonlinear term. The formulation is developed within the de BroglieBohm framework, considering an adimensional phase. The resulting equations include a modified continuity equation and a quantum Hamilton–Jacobi structure.

May 8, 20260 citations

Nonlinear Dissipative Schr¨odinger Equation for Deep Ocean Wave Collapse and its Bohmian Feynman Propagator

Daniel Gemaque da Silva

Anonlinear dissipative Schr¨odinger equation describing deep ocean wave collapse is proposed within the hydrodynamic De Broglie-Bohm framework. The probability density is interpreted as the intensity of deep ocean waves. The model generates simultaneously a dissipative continuity equation and a dissipative Euler equation. A unique exponential variable transformation converts both equations into conservative forms. The associated Bohmian Feynman propagator is constructed through the effective action formalism and path integral approach. The model naturally describes focusing collapse, rogue-wave amplification, nonlinear dissipation, and hydrodynamic quantum trajectories.

May 9, 20260 citations

Nonlinear Non-Dissipative Schr¨odinger Equation for Geyser-Type Oceanic Waves in the de Broglie–Bohm Hydrodynamic Formalism

Daniel Gemaque Gemaque da Silva

Abstract In this work we propose a nonlinear non-dissipative Schr¨odinger equation capable of describing geyser-type oceanic wave structures within the de Broglie–Bohm hydrodynamic formalism. The model is constructed assuming a conservative continuity equation and a conservative Euler equation. The wave intensity is interpreted as an oceanic wave density field. A periodic nonlinear interaction term is introduced in order to generate eruptive and pulsating wave dynamics similar to geyser structures. The corresponding Bohm quantum potential and hydrodynamic equations are derived explicitly.

Jan 1, 20260 citations