Adiabatic soliton management: Controlling solitary wave motion while keeping the wave envelope unchanged
Abstract
We describe how to control the motion -- both speed and propagation direction -- of a nonlinear traveling wave in real time via soliton management with time-varying dispersion/diffusion and loss/gain terms. When carried out subject to certain parameter constraints we derive, the approach allows for real-time manipulation of wave motion without compromising the structure or stability of the wave, maintaining strict adiabaticity in time. This makes our approach a promising tool for physical systems which admit a degree of control through adjustable dispersion and loss/gain terms, including problems arising in nonlinear optics, atomic physics, Bose-Einstein condensates, and thermally driven chemical reactions, where one is interested in modifying the position or speed of a wave while still maintaining adiabaticity. We illustrate both the utility and simplicity of the method through several canonical examples, demonstrating how the motion of KdV solitons, Fisher-KPP solitary wavefronts, BBM solitons, nonlinear Klein-Gordon equations, and interacting nonlinear waves in a vector NLS system can be controlled in real time.
Keywords
Cite
@article{arxiv.2107.07619,
title = {Adiabatic soliton management: Controlling solitary wave motion while keeping the wave envelope unchanged},
author = {Robert A. Van Gorder},
journal= {arXiv preprint arXiv:2107.07619},
year = {2022}
}