Conservative Dissipative Bohm–Schrödinger Equation: A Hydrodynamic Nonlinear Model with Solitonic Oceanic Interpretation

Daniel Gemaque da Silva

Published May 8, 2026• 0 citations

Abstract

In this work we propose a nonlinear dissipative Schrödinger equation preserving both the continuity equation and the Euler equation within the de Broglie–Bohm hydrodynamic formalism. The model introduces a structural dissipative term acting on the density gradients without violating global probability conservation. We derive the corresponding Madelung equations, analyze solitonic solutions, obtain a dissipative dispersion relation, and discuss an effective hydrodynamic interpretation for oceanic solitary waves. The equation naturally reduces to nonlinear Schrödingertype and Korteweg–de Vries-type dissipative equations under suitable approximations.

DOI: 10.5281/zenodo.20078121

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