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Solitary waves and Bohmian mechanics.
Alberto Abbondandolo1, Vieri Benci
1Scula Normale Superiore, Piazza dei Cavalieri 7, 56126 Pisa, Italy. abbo@tonelli.sns.it
Summary
This study introduces a nonlinear Schrödinger-like equation that generates stable, concentrated topological solitary waves. These waves exhibit Bohmian mechanics, offering a nonsingular model of de Broglie pilot wave theory.
Area of Science:
- Quantum mechanics
- Nonlinear dynamics
- Mathematical physics
Background:
- Schrödinger equation describes quantum systems.
- Nonlinearities introduce complex phenomena.
- Topological structures in physics are of significant interest.
Purpose of the Study:
- To investigate a nonlinear Schrödinger-like equation.
- To explore the existence and behavior of solitary waves.
- To establish a connection with pilot wave theory.
Main Methods:
- Analysis of a modified Schrödinger equation with a nonlinear term.
- Mathematical modeling of solitary wave solutions.
- Comparison of wave dynamics with Bohmian mechanics.
Main Results:
- Existence of stable, highly concentrated solitary waves with topological properties.
- Demonstration that these solitary waves follow Bohmian trajectories.
- Development of a nonsingular realization of de Broglie pilot wave theory.
Conclusions:
- The nonlinear term is crucial for stable topological solitary waves.
- The model provides a novel, singularity-free interpretation of pilot wave theory.
- This work bridges nonlinear dynamics and foundational quantum mechanics.