Search results for "SOLITONS"

Numerical study of a multiscale expansion of the Korteweg de Vries equation and Painlev\'e-II equation

2007

The Cauchy problem for the Korteweg de Vries (KdV) equation with small dispersion of order $\e^2$, $\e\ll 1$, is characterized by the appearance of a zone of rapid modulated oscillations. These oscillations are approximately described by the elliptic solution of KdV where the amplitude, wave-number and frequency are not constant but evolve according to the Whitham equations. Whereas the difference between the KdV and the asymptotic solution decreases as $\epsilon$ in the interior of the Whitham oscillatory zone, it is known to be only of order $\epsilon^{1/3}$ near the leading edge of this zone. To obtain a more accurate description near the leading edge of the oscillatory zone we present a…

Cellular automaton for chimera states

2016

A minimalistic model for chimera states is presented. The model is a cellular automaton (CA) which depends on only one adjustable parameter, the range of the nonlocal coupling, and is built from elementary cellular automata and the majority (voting) rule. This suggests the universality of chimera-like behavior from a new point of view: Already simple CA rules based on the majority rule exhibit this behavior. After a short transient, we find chimera states for arbitrary initial conditions, the system spontaneously splitting into stable domains separated by static boundaries, ones synchronously oscillating and the others incoherent. When the coupling range is local, nontrivial coherent struct…

Comment on "Dynamics and properties of waves in a modified Noguchi electrical transmission line"

2016

A recent paper [Phys. Rev. E 91, 022925 (2015)PRESCM1539-375510.1103/PhysRevE.91.022925] presents the derivation of the nonlinear equation modeling envelope waves in a specific case of band passed filter discrete nonlinear electrical transmission line (NLTL), called "A modified Noguchi electrical transmission line" according to the authors. Using the reductive perturbation approach in the semidiscrete approximation, they showed that the modulated waves propagating in this NLTL are described by the ordinary nonlinear Schrodinger (NLS) equation. On the basis of their results, the authors claimed that all previous works on the band passed filter NLTL, which considered the vanishing of the dc c…

Dissipative soliton interactions inside a fiber laser cavity

2005

We report our recent numerical and experimental observations of dissipative soliton interactions inside a fiber laser cavity. A bound state, formed from two pulses, may have a group velocity which differs from that of a single soliton. As a result, they can collide inside the cavity. This results in a variety of outcomes. Numerical simulations are based either on a continuous model or on a parameter-managed model of the cubic-quintic Ginzburg-Landau equation. Each of the models provides explanations for our experimental observations. © 2005 Elsevier Inc. All rights reserved.

Soliplasmon excitations at metal/dielectric/Kerr structures

2009

We present novel optical phenomena based on the existence of a new type of quasi-particle excitation in metal/dielectric/Kerr structures. We discuss the possibility of excitation of surface plasmon polaritons via spatial solitons in these systems.

Quantized separations of phase-locked soliton pairs in fiber lasers

2003

Quantized separations of phase-locked soliton pairs in fiber lasers were presented. The relation between the Kelly sidebands and the quantized separations between solitons was confirmed. Simulation results showed that the solitons can see each other at relatively larger distances than they would in the absence of radiation.

Compact-envelope bright solitary wave in a DNA double strand

2012

International audience; We study the nonlinear dynamics of a homogeneous DNA chain which is based on site-dependent finite stacking and pairing enthalpies. We introduce an extended nonlinear Schroedinger equation describing the dynamics of modulated waves in DNA model. We obtain envelope bright solitary waves with compact support as a solution. Analytical criteria of existence and stability of this solution are derived. The stability of bright compactons is confirmed by numerical simulations of the exact equations of the lattice. The impact of the fi nite stacking energy is investigated and we show that some of these compact bright solitary waves are very robust, while others decompose quic…

Observation of Manakov polarization modulation instability in the normal dispersion regime of randomly birefringent telecom optical fiber

2014

Stabilization of 1D solitons by fractional derivatives in systems with quintic nonlinearity

2022

AbstractWe study theoretically the properties of a soliton solution of the fractional Schrödinger equation with quintic nonlinearity. Under “fractional” we understand the Schrödinger equation, where ordinary Laplacian (second spatial derivative in 1D) is substituted by its fractional counterpart with Lévy index $$\alpha$$ α . We speculate that the latter substitution corresponds to phenomenological account for disorder in a system. Using analytical (variational and perturbative) and numerical arguments, we have shown that while in the case of Schrödinger equation with the ordinary Laplacian (corresponding to Lévy index $$\alpha =2$$ α = 2 ), the soliton is unstable, even infinitesimal diffe…

Propagation, Stability and Interactions of Novel Three-Wave Parametric Solitons

2006

International audience; We found a new class of analytic soliton solutions that describe the parametric wave mixing of optical pulses in quadratic nonlinear crystals. We analyze the stability properties, interactions and collisions of these solitons.