# Peregrine Soliton with Controllable Center in the Causal Interpretation of Quantum Mechanics

Peregrine Soliton with Controllable Center in the Causal Interpretation of Quantum Mechanics

The standard "self-focusing" nonlinear Schrödinger equation, also known as the Gross–Pitaevskii equation, appears in wave propagation through nonlinear media such as signal transmission in optical fibers, Bose–Einstein condensation, and surface waves over sufficiently deep water. This Demonstration studies a spatially localized algebraic breather solution (Peregrine soliton), where the maximum of the squared wavefunction varies by initial conditions. The causal interpretation of quantum theory developed by Louis de Broglie and David Bohm introduced trajectories that are guided by a quantum potential. The velocities of single particles, following the trajectories, are determined by the phase of the wavefunction. The system is time reversible.

In the graphic on the left, you can see the position of the particles (blue), the squared wavefunction (blue), the quantum potential (red), and the velocity (orange). On the right, the graphic shows the squared wavefunction plus trajectories.