Search results for "Integrable systems"
showing 10 items of 256 documents
Inelastic scattering and interactions of three-wave parametric solitons.
2006
We study the interactions of velocity-locked three-wave parametric solitons in a medium with quadratic nonlinearity and dispersion. We reveal that the inelastic scattering between three-wave solitons and linear waves may be described in terms of analytical solutions with dynamically varying group velocity, or boomerons. Moreover, we demonstrate the elastic nature of three-wave soliton-soliton collisions and interactions.
Dark-and-bright rogue waves in long wave-short wave resonance
2014
Nonlinear Photonics, Bragg Gratings, Photosensitivity, and Poling in Glass Waveguides, in Proceedings Advanced Photonics, Part of Advanced Photonics, Barcelona, Spain, 28-31 July 2014
Finite-temperature correlations in the one-dimensional trapped and untrapped Bose gases
2003
We calculate the dynamic single-particle and many-particle correlation functions at non-zero temperature in one-dimensional trapped repulsive Bose gases. The decay for increasing distance between the points of these correlation functions is governed by a scaling exponent that has a universal expression in terms of observed quantities. This expression is valid in the weak-interaction Gross-Pitaevskii as well as in the strong-interaction Girardeau-Tonks limit, but the observed quantities involved depend on the interaction strength. The confining trap introduces a weak center-of-mass dependence in the scaling exponent. We also conjecture results for the density-density correlation function.
Optical solitons in erbium doped fibers with higher order effects
2000
Abstract We consider the coupled system of higher order nonlinear Schrodinger equation and Maxwell–Bloch (HNLS–MB) equations, which governs the nonlinear wave propagation in erbium doped optical waveguides in presence of important higher order effects. We present the Lax pair and using Backlund transformation exact soliton solutions are generated.
Impurity effects on soliton dynamics in planar ferromagnets
1993
Abstract We investigate numerically the dynamics of solitons in a ferromagnetic spin chain and we show that the sine-Gordon approximation provides only a poor description of the solitary excitations in the presence of impurities. Depending on their energy and the strength of the impurity, solitons can be reflected or transmitted. When they are reflected, they can suffer abrupt changes in velocity, which are associated to the switch from one soliton branch to another. In some cases the scattering by an impurity can excite an internal mode of the soliton, which is able to store some energy and modify the output of the scattering.
Multipole solitary wave solutions of the higher-order nonlinear Schrödinger equation with quintic non-Kerr terms
2013
We consider a high-order nonlinear Schrodinger (HNLS) equation with third- and fourth-order dispersions, quintic non-Kerr terms, self steepening, and self-frequency-shift effects. The model applies to the description of ultrashort optical pulse propagation in highly nonlinear media. We propose a complex envelope function ansatz composed of single bright, single dark and the product of bright and dark solitary waves that allows us to obtain analytically different shapes of solitary wave solutions. Parametric conditions for the existence and uniqueness of such solitary waves are presented. The solutions comprise fundamental solitons, kink and anti-kink solitons, W-shaped, dipole, tripole, and…
Slow-light solitons: Influence of relaxation
2008
We have applied the transformation of the slow-light equations to the Liouville theory that we developed in our previous work, to study the influence of relaxation on the soliton dynamics. We solved the problem of the soliton dynamics in the presence of relaxation and found that the spontaneous emission from the upper atomic level is strongly suppressed. Our solution proves that the spatial shape of the soliton is well preserved even if the relaxation time is much shorter than the soliton time length. This fact is of great importance for applications of the slow-light soliton concept in optical information processing. We also demonstrate that relaxation plays a role of resistance to the sol…
Nearly-integrable dissipative systems and celestial mechanics
2010
The influence of dissipative effects on classical dynamical models of Celestial Mechanics is of basic importance. We introduce the reader to the subject, giving classical examples found in the literature, like the standard map, the Hénon map, the logistic mapping. In the framework of the dissipative standard map, we investigate the existence of periodic orbits as a function of the parameters. We also provide some techniques to compute the breakdown threshold of quasi-periodic attractors. Next, we review a simple model of Celestial Mechanics, known as the spin-orbit problem which is closely linked to the dissipative standard map. In this context we present the conservative and dissipative KA…
Bright and dark optical solitons in fiber media with higher-order effects
2002
We consider N-coupled higher-order nonlinear Schrodinger (N-CHNLS) equations which govern the simultaneous propagation of N optical fields in fiber media with higher-order effects. Bright and dark soliton solutions are derived using Hirota bilinear method for the general cross-coupling ratio between the parameters of self-phase modulation and cross-phase modulation effects. By means of coupled amplitude-phase formulation also, similar kind of dark soliton solutions are obtained. It is found that the parametric conditions for the simultaneous propagation of N dark solitons from both the methods are the same.
Optimized Hermite-Gaussian ansatz functions for dispersion-managed solitons
2001
Abstract By theoretical analysis, we show that the usual procedure of simply projecting the dispersion-managed (DM) soliton profile onto the basis of an arbitrary number of Hermite-gaussian (HG) polynomials leads to relatively accurate ansatz functions, but does not correspond to the best representation of DM solitons. Based on the minimization of the soliton dressing, we present a simple procedure, which provides highly accurate representation of DM solitons on the basis of a few HG polynomials only.