Adiabatic soliton management: Controlling solitary wave motion while keeping the wave envelope unchanged

• Main Author: Van Gorder, R.A (Author)
• Format: Article
• Language: English
• Published: Elsevier B.V. 2022
• Subjects: Adiabaticity; Atomic physics; Bose-Einstein condensation; Dispersion (waves); Dispersion management; Dispersion-management; Equations of motion; Nonlinear equations; Nonlinear optics; Nonlinear travelling waves; Propagation direction; Real- time; Soliton management; Solitons; Statistical mechanics; Wave envelope; Wave motions; Wavefronts; Wavespeed; Wavespeed control
• Online Access: View Fulltext in Publisher

 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. © 2022 Elsevier B.V.