Ubiquitous nonlinear waves in dispersive media include localized solitons and extended hydrodynamic states such as dispersive shock waves. Despite their physical prominence and the development of thorough theoretical and experimental investigations of each separately, experiments and a unified theory of solitons and dispersive hydrodynamics are lacking. Here, a general soliton-mean field theory is introduced and used to describe the propagation of solitons in macroscopic hydrodynamic flows. Two universal adiabatic invariants of motion are identified that predict trapping or transmission of solitons by hydrodynamic states. The result of solitons incident upon smooth expansion waves or compressive, rapidly oscillating dispersive shock waves is the same, an effect termed hydrodynamic reciprocity. Experiments on viscous fluid conduits quantitatively confirm the soliton-mean field theory with broader implications for nonlinear optics, superfluids, geophysical fluids, and other dispersive hydrodynamic media.
The interaction behavior of solitons are defining characteristics of these nonlinear, coherent structures. Due to recent experimental observations, thin ferromagnetic films offer a promising medium in which to study the scattering properties of two-dimensional magnetic droplet solitons, particlelike, precessing dipoles. Here, a rich set of two-droplet interaction behaviors are classified through micromagnetic simulations. Repulsive and attractive interaction dynamics are generically determined by the relative phase and speeds of the two droplets and can be classified into four types: (1) merger into a breather bound state, (2) counterpropagation trapped along the axis of symmetry, (3) reflection, and (4) violent droplet annihilation into spin wave radiation and a breather. Utilizing a nonlinear method of images, it is demonstrated that these dynamics describe repulsive/attractive scattering of a single droplet off of a magnetic boundary with pinned/free spin boundary conditions, respectively. These results explain the mechanism by which propagating and stationary droplets can be stabilized in a confined ferromagnet.Solitary waves or solitons are particle-like wave packets that arise in a wide range of physical contexts from a balance between dispersive spreading and nonlinear focusing. One of the key phenomena that differentiates nonlinear coherent structures such as solitons from their linear counterparts is what happens when such structures interact. Soliton solutions of equations with very special mathematical structure (integrability) have been shown to interact elastically [1] and can be attractive or repulsive [2]. In more general systems, soliton interactions can be significantly more complex, exhibiting fusion, fission, annihilation, or spiraling [3,4]. A relative phase between the solitons plays a dominant role in determining the resulting interaction behaviors. An additional interaction feature, 90• scattering, has been predicted for twodimensional (2D) magnetic solitons [5,6] and solitons in field theories [7,8]. The recent experimental observation of a magnetic droplet soliton in a spatially extended film [9] provides the impetus for our deeper study of magnetic soliton interactions. Here, we show that the interaction of a pair of 2D magnetic droplet solitons (from here on in, droplets) exhibits rich behavior, principally dependent on the droplets' relative phase.Previous studies of soliton interaction in 2D ferromagnetic materials have concentrated primarily on vortices, topological structures that exhibit restricted dynamics [10]. Unless the ferromagnet is confined [11], conservation of overall topological charge pins the magnetic "center of mass" in place, e.g. a single vortex core, limiting motion to rotating collections [5,12] or linear motion of vortex pairs with net zero topological charge. Perpendicular scattering of two interacting vortex pairs has been theoretically demonstrated [6]. It appears that 90• scattering has a more universal character [8], not requiring a topological charge, and p...
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.
hi@scite.ai
10624 S. Eastern Ave., Ste. A-614
Henderson, NV 89052, USA
Copyright © 2024 scite LLC. All rights reserved.
Made with 💙 for researchers
Part of the Research Solutions Family.