Search results for "Nonlinear"
showing 10 items of 3684 documents
Multimode emission in inhomogeneously broadened ring lasers
2001
The threshold for multilongitudinal-mode emission in inhomogeneously broadened ring lasers is analytically investigated. In the homogeneous limit the multimode instability corresponds to the classical Risken–Nummedal–Graham–Haken instability. It is found that by increasing the inhomogeneous linewidth, the instability threshold is decreased and the growth of high-frequency side modes is favored. In the limit where the population-inversion decay rate γ‖ is much smaller than the polarization decay rate γ⊥ (class B lasers), analytical expressions for the instability threshold are found, which are then generalized to three-level lasers for a comparison with experimental results obtained with erb…
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…
Effect of the Converging Pipe on the Performance of a Lucid Spherical Rotor
2018
Lucid spherical rotor is a cross-flow rotor developed to be installed within a pipeline. The purpose of installing this type of rotor is to collect excess energy available in gravity-fed water pipelines. In order to enhance the efficiency of the rotor which is installed in a channel, this paper aims to study the performance of Lucid spherical rotor with converging pipe. Numerical investigations were carried out to analyze the effect of the converging pipe on the performance of the rotor. Numerical simulations have been carried out using the unsteady Reynolds-averaged Navier–Stokes equations in conjunction with the realizable $$k-{\varepsilon }$$ turbulence model. The validation of the numer…
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.
The fifth order Peregrine breather and its eight-parameters deformations solutions of the NLS equation.
2013
We construct here explicitly new deformations of the Peregrine breather of order 5 with 8 real parameters. This gives new families of quasi-rational solutions of the NLS equation and thus one can describe in a more precise way the phenomena of appearance of multi rogue waves. With this method, we construct new patterns of different types of rogue waves. We get at the same time, the triangular configurations as well as rings isolated. Moreover, one sees appearing for certain values of the parameters, new configurations of concentric rings.
High-order harmonic generation in fullerenes using few- and multi-cycle pulses of different wavelengths
2012
We present the results of experimental and theoretical studies of high-order harmonic generation (HHG) in plasmas containing fullerenes using pulses of different duration and wavelength. We find that the harmonic cutoff is extended in the case of few-cycle pulses (3.5 fs, 29th harmonic) compared to longer laser pulses (40 fs, 25th harmonic) at the same intensity. Our studies also include HHG in fullerenes using 1300 and 780 nm multicycle (35 and 40 fs) pulses. For 1300 nm pulses, an extension of the harmonic cutoff to the 41st order was obtained, with a decrease in conversion efficiency that is consistent with theoretical predictions based on wave packet spreading for single atoms. Theoreti…
Electron dynamical response in InP semiconductors driven by fluctuating electric fields
2015
Abstract The complexity of electron dynamics in low-doped n-type InP crystals operating under fluctuating electric fields is deeply explored and discussed. In this study, we employ a multi-particle Monte Carlo approach to simulate the non-linear transport of electrons inside the semiconductor bulk. All possible scattering events of hot electrons in the medium, the main details of the band structure, as well as the heating effects, are taken into account. The results presented in this study derive from numerical simulations of the electron dynamical response to the application of a sub-Thz electric field, fluctuating for the superimposition of an external source of Gaussian correlated noise.…
Spatial Soliton Dynamics in Two-Dimensional Quadratic Photonic Crystals
2007
We present a theoretical and experimental investigation of soliton dynamics associated to twin-beam second harmonic generation in a purely nonlinear two-dimensional planar photonic lattice in LiNbO3.
q-deformed solitons and quantum solitons of the Maxwell-Bloch lattice
2000
We report for the first time exact solutions of a completely integrable nonlinear lattice system for which the dynamical variables satisfy a q-deformed Lie algebra - the Lie-Poisson algebra su_q(2). The system considered is a q-deformed lattice for which in continuum limit the equations of motion become the envelope Maxwell-Bloch (or SIT) equations describing the resonant interaction of light with a nonlinear dielectric. Thus the N-soliton solutions we here report are the natural q-deformations, necessary for a lattice, of the well-known multi-soliton and breather solutions of self-induced transparency (SIT). The method we use to find these solutions is a generalization of the Darboux-Backl…
Statistical Mechanics of the Sine-Gordon Equation
1986
We give two fundamental methods for evaluation of classical free energies of all the integrable models admitting soliton solutions; the sine-Gordon equation is one example. Periodic boundary conditions impose integral equations for allowed phonon and soliton momenta. From these, generalized Bethe-Ansatz and functional-integration methods using action-angle variables follow. Results for free energies coincide, and coincide with those that we find by transfer-integral methods. Extension to the quantum case, and quantum Bethe Ansatz, on the lines to be reported elsewhere for the sinh-Gordon equation, is indicated.