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

Key Points

• This research aims to develop a nonlinear Schrödinger equation that incorporates oceanic-type nonlinearity in a Bohmian framework.
• Developed a nonlinear Schrödinger equation with an oceanic-type nonlinear term.
• Formulated within the de Broglie-Bohm framework considering an adimensional phase.
• Included a modified continuity equation and quantum Hamilton–Jacobi structure.
• Proposed equations enhance understanding of quantum systems with nonlinear interactions.
• The inclusion of an oceanic structure reveals unique dynamic behaviors.
• The modified continuity and Hamilton–Jacobi equations provide a new mathematical framework for quantum mechanics.