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

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.