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.
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.
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.
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.
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.
In this work we propose a nonlinear dissipative Schr¨odinger equation applied to the description of geyser-type ocean waves within the hydrodynamic De BroglieBohm framework. The model considers the probability density as the physical intensity of the ocean wave, simultaneously introducing dissipation, local amplification, and hydrodynamic nonlinearity. Using the Madelung–Bohm decomposition, we derive a dissipative continuity equation and a dissipative Euler equation. Furthermore, we demonstrate that the system admits a transformation into an equivalent conservative structure through an exponential variable transformation. Finally, we construct sech-type solitonic solutions representing coherent oceanic jets similar to hydrodynamic geysers.