Nonlinear Dissipative Schr¨odinger Model for Geyser-Type Ocean Waves with Solitonic Structures in the De Broglie–Bohm Formalism

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.