Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userInternal modes of oscillations of topological solitons in highly dispersive media
68
0
0.0
(
0
)
Ask ChatGPT about the research
No Arabic abstract
The problem of stability and spectrum of linear excitations of a soliton (kink) of the dispersive sine-Gordon and $varphi^4$ - equations is solved exactly. It is shown that the total spectrum consists of a discrete set of frequencies of internal modes and a single band spectrum of continuum waves. It is indicated by numerical simulations that a translation motion of a single soliton in the highly dispersive systems is accompanied by the arising of its internal dynamics and, in some cases, creation of breathers, and always by generation of the backward radiation. It is shown numerically that a fast motion of two topological solitons leads to a formation of the bound soliton complex in the dispersive sine-Gordon system.
rate research
Read More
We determine the functional behavior near the discrete rotational symmetry axis of discrete vortices of the nonlinear Schrodinger equation. We show that these solutions present a central phase singularity whose charge is restricted by symmetry arguments. Consequently, we demonstrate that the existence of high-charged discrete vortices is related to the presence of other off-axis phase singularities, whose positions and charges are also restricted by symmetry arguments. To illustrate our theoretical results, we offer two numerical examples of high-charged discrete vortices in photonic crystal fibers showing hexagonal discrete rotational invariance.
We examine the evolution of a time-varying perturbation signal pumped into a mono-mode fiber in the anomalous dispersion regime. We analytically establish that the perturbation evolves into a conservative pattern of periodic pulses which structures and profiles share close similarity with the so-called soliton-crystal states recently observed in fiber media [see e.g. A. Haboucha et al., Phys. Rev. Atextbf{78}, 043806 (2008); D. Y. Tang et al., Phys. Rev. Lett. textbf{101}, 153904 (2008); F. Amrani et al., Opt. Express textbf{19}, 13134 (2011)]. We derive mathematically and generate numerically a crystal of solitons using time division multiplexing of identical pulses. We suggest that at very fast pumping rates, the pulse signals overlap and create an unstable signal that is modulated by the fiber nonlinearity to become a periodic lattice of pulse solitons which can be described by elliptic functions. We carry out a linear stability analysis of the soliton-crystal structure and establish that the correlation of centers of mass of interacting pulses broadens their internal-mode spectrum, some modes of which are mutually degenerate. While it has long been known that high-intensity periodic pulse trains in optical fibers are generated from the phenomenon of modulational instability of continuous waves, the present study provides evidence that they can also be generated via temporal multiplexing of an infinitely large number of equal-intensity single pulses to give rise to stable elliptic solitons.
The theory of optical dispersive shocks generated in propagation of light beams through photorefractive media is developed. Full one-dimensional analytical theory based on the Whitham modulation approach is given for the simplest case of sharp step-like initial discontinuity in a beam with one-dimensional strip-like geometry. This approach is confirmed by numerical simulations which are extended also to beams with cylindrical symmetry. The theory explains recent experiments where such dispersive shock waves have been observed.
The possibility of tailoring the guidance properties of optical fibers along the same direction as the evolution of the optical field allows to explore new directions in nonlinear fiber optics. The new degree of freedom offered by axially-varying optical fibers enables to revisit well-established nonlinear phenomena, and even to discover novel short pulse nonlinear dynamics. Here we study the impact of meter-scale longitudinal variations of group velocity dispersion on the propagation of bright solitons and on their associated dispersive waves. We show that the longitudinal tailoring of fiber properties allows to observe experimentally unique dispersive waves dynamics, such as the emission of cascaded, multiple or polychromatic dispersive waves.
We consider the step Riemann problem for the system of equations describing the propagation of a coherent light beam in nematic liquid crystals, which is a general system describing nonlinear wave propagation in a number of different physical applications. While the equation governing the light beam is of defocusing nonlinear Schrodinger equation type, the dispersive shock wave (DSW) generated from this initial condition has major differences from the standard DSW solution of the defocusing nonlinear Schrodinger equation. In particular, it is found that the DSW has positive polarity and generates resonant radiation which propagates ahead of it. Remarkably, the velocity of the lead soliton of the DSW is determined by the classical shock velocity. The solution for the radiative wavetrain is obtained using the WKB approximation. It is shown that for sufficiently small initial jumps the nematic DSW is asymptotically governed by a Korteweg-de Vries equation with fifth order dispersion, which explicitly shows the resonance generating the radiation ahead of the DSW. The constructed asymptotic theory is shown to be in good agreement with the results of direct numerical simulations.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
