Propagation and ramification of a solitary pulse through an environmentally coupled qubit

In this paper a new kind of device — a gradient distributed fiber amplifier — is proposed and analysed. In such an amplifier the concentration of the dopant ions increases along its length in the direction of pump power decrement, in a way that ensures nearly constant signal gain coefficient in every point of the fiber. Hence, an optimal amplification configuration that simultaneously stabilises the pulses against the background attenuation, the soliton self- frequency shift and the third order dispersion can be chosen and maintained globally in such a device. The results of the computer model clearly show that a gradient fiber amplifier can be designed as a completely transparent transport media for high-speed, long distance optical fiber communications.

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Solitons in an ion-beam plasma

Journal of Plasma Physics ◽

10.1017/s0022377800012976 ◽

1988 ◽

Vol 39 (2) ◽

pp. 183-191 ◽

Cited By ~ 28

Author(s):

G. P. Zank ◽

J. F. McKenzie

Keyword(s):

Ion Beam ◽

Finite Amplitude ◽

Total Momentum ◽

Plasma System ◽

Weakly Nonlinear ◽

Classical Energy ◽

Convective Instabilities ◽

Beam Plasma ◽

Solitary Pulse ◽

Wave Profiles

It is shown that the conservation law for total momentum of an ion-beam plasma system can be cast in the form of a classical energy integral of a particle in a potential well. By using boundary conditions appropriate to a solitary pulse, we derive conditions for the existence of finite-amplitude solitons propagating in the system. Under suitable conditions, as many as three forward-propagating solitary waves can exist. It is interesting to note that the criterion for their existence is intimately related to the absence of convective instabilities in an ion-beam plasma. Exact ‘sech2’ type solutions are available in the weakly nonlinear regime. Solitary-wave profiles for the general case are obtained numerically.

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On the structure of collisionless waves

Journal of Plasma Physics ◽

10.1017/s0022377800004712 ◽

1969 ◽

Vol 3 (4) ◽

pp. 673-689 ◽

Cited By ~ 7

Author(s):

James B. Fedele

Keyword(s):

Magnetic Field ◽

Applied Magnetic Field ◽

Small Amplitude ◽

Single Mode ◽

Larmor Radius ◽

Collisionless Shock ◽

Finite Larmor Radius ◽

First Order ◽

Pulse Solution ◽

Solitary Pulse

Small amplitude waves and collisionless shock waves are investigated within the framework of the first-order Chew—Goldberger—Low equations. For linearized oscillations, two modes are present for propagation along an applied magnetic field. One is an acoustic type which contains no finite Larmor radius effects. The other which contains the ‘fire hose’ instability in its lowest order terms, does possess finite Larmor radius corrections. These corrections, however, do not produce instabilities or dissipation. There are no finite Larmor radius corrections to the single mode present for propagation normal to the applied magnetic field. Normal shock structure is investigated, but it is shown that jump solutions do not exist. An analytic solitary pulse solution is found and is compared with the Adlam—Allen pulse solution.

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Traveling and solitary waves in monodisperse and dimer granular chains

International Journal of Modern Physics B ◽

10.1142/s0217979217420012 ◽

2017 ◽

Vol 31 (10) ◽

pp. 1742001 ◽

Cited By ~ 1

Author(s):

Yuli Starosvetsky ◽

K. R. Jayaprakash ◽

Alexander F. Vakakis

Keyword(s):

Solitary Wave ◽

Solitary Waves ◽

Traveling Waves ◽

Granular Media ◽

Equations Of Motion ◽

Continuum Approximation ◽

Granular Chains ◽

Solitary Pulse ◽

Countably Infinite ◽

Dimer Granular Chains

We provide a review of propagating traveling waves and solitary pulses in uncompressed one-dimensional ([Formula: see text]) ordered granular media. The first such solution in homogeneous granular media was discovered by Nesterenko in the form of a single-hump solitary pulse with energy-dependent profile and velocity. Considering directly the discrete, strongly nonlinear governing equations of motion of these media (i.e., without resorting to continuum approximation or homogenization), we show the existence of countably infinite families of stable multi-hump propagating traveling waves with arbitrary wavelengths. A semi-analytical approach is used to study the dependence of these waves on spatial periodicity (wavenumber) and energy, and to show that in a certain asymptotic limit, these families converge to the single-hump Nesterenko solitary wave. Then the study is extended in dimer granular chains composed of alternating “heavy” and “light” beads. For a set of specific mass ratios between the light and heavy beads, we show the existence of multi-hump solitary waves that propagate faster than the Nesterenko solitary wave in the corresponding homogeneous granular chain composed of only heavy beads. The existence of these waves has interesting implications in energy transmission in ordered granular chains.

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Interaction dynamics of solitary waves on a falling film

Journal of Fluid Mechanics ◽

10.1017/s0022112095002837 ◽

1995 ◽

Vol 294 ◽

pp. 123-154 ◽

Cited By ~ 56

Author(s):

H.-C. Chang ◽

E. Demekhin ◽

E. Kalaidin

Keyword(s):

Solitary Waves ◽

Structure Theory ◽

Binary Interaction ◽

Falling Film ◽

Wave Dynamics ◽

Localized Structures ◽

Physical Experiments ◽

Solitary Pulse ◽

Short Transition ◽

Simple Dynamical System

Beyond a short transition region near the inlet, waves on a falling film evolve into distinct pulse-like solitary waves that dominate all subsequent interfacial dynamics. Numerical and physical experiments indicate that these localized structures can attract and repel each other. Attractive interaction through the capillary ripples of the pulses causes two pulses to coalesce into a bigger pulse which accelerates and precipitates further coalescence. This binary interaction between an ‘excited’ pulse after coalescence and its smaller front neighbour is the key mechanism that drives the observed wave dynamics. From symmetry arguments, two dominant modes for a solitary pulse are obtained and used to develop an inelastic coherent structure theory for binary interaction between an excited pulse and its front neighbour. The theory offers a simple dynamical system that quantitatively describes the binary interaction and promises to elucidate the complex wave dynamics on a falling film.

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Bifurcation analysis of the propagation of femtosecond pulses for the Triki-Biswas equation in monomode optical fibers

International Journal of Modern Physics B ◽

10.1142/s0217979219503466 ◽

2019 ◽

Vol 33 (29) ◽

pp. 1950346 ◽

Cited By ~ 1

Author(s):

Asit Saha

Keyword(s):

Optical Fibers ◽

Bifurcation Analysis ◽

Phase Plane ◽

Dynamical Behavior ◽

Phase Plane Analysis ◽

Femtosecond Pulses ◽

Plane Analysis ◽

Solitary Pulse ◽

Time Series Plot ◽

First Time

Bifurcation analysis of the propagation of femtosecond pulses for the Triki–Biswas (TB) equation in monomode optical fibers is reported for the first time. Bifurcation of phase plots of the dynamical system is dispensed using phase plane analysis through symbolic computation. It is observed that the TB equation supports femtosecond solitary pulse, periodic pulse, superperiodic pulse, kink and anti-kink pulses, which are presented through time series plot numerically. Analytical forms of the femtosecond solitary pulses are obtained. This contribution may be applicable to interpret the dynamical behavior of various femtosecond pulses in monomode optical fibers beyond the Kerr limit.

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Two-dimensional pulse dynamics and the formation of bound states on electrified falling films

Journal of Fluid Mechanics ◽

10.1017/jfm.2018.592 ◽

2018 ◽

Vol 855 ◽

pp. 210-235 ◽

Cited By ~ 6

Author(s):

M. G. Blyth ◽

D. Tseluiko ◽

T.-S. Lin ◽

S. Kalliadasis

Keyword(s):

Electric Field ◽

Bound States ◽

Stokes Equations ◽

Travelling Waves ◽

Film Surface ◽

Wave Model ◽

Bound State ◽

Long Wave ◽

Finite Set ◽

Solitary Pulse

The flow of an electrified liquid film down an inclined plane wall is investigated with the focus on coherent structures in the form of travelling waves on the film surface, in particular, single-hump solitary pulses and their interactions. The flow structures are analysed first using a long-wave model, which is valid in the presence of weak inertia, and second using the Stokes equations. For obtuse angles, gravity is destabilising and solitary pulses exist even in the absence of an electric field. For acute angles, spatially non-uniform solutions exist only beyond a critical value of the electric field strength; moreover, solitary-pulse solutions are present only at sufficiently high supercritical electric-field strengths. The electric field increases the amplitude of the pulses, can generate recirculation zones in the humps and alters the far-field decay of the pulse tails from exponential to algebraic with a significant impact on pulse interactions. A weak-interaction theory predicts an infinite sequence of bound-state solutions for non-electrified flow, and a finite set for electrified flow. The existence of single-hump pulse solutions and two-pulse bound states is confirmed for the Stokes equations via boundary-element computations. In addition, the electric field is shown to trigger a switch from absolute to convective instability, thereby regularising the dynamics, and this is confirmed by time-dependent simulations of the long-wave model.

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