Search results for "Nonlinear Schrö"
showing 10 items of 86 documents
Hydrodynamics of periodic breathers
2014
We report the first experimental observation of periodic breathers in water waves. One of them is Kuznetsov–Ma soliton and another one is Akhmediev breather. Each of them is a localized solution of the nonlinear Schrödinger equation (NLS) on a constant background. The difference is in localization which is either in time or in space. The experiments conducted in a water wave flume show results that are in good agreement with the NLS theory. Basic features of the breathers that include the maximal amplitudes and spectra are consistent with the theoretical predictions.
Tenth Peregrine breather solution to the NLS equation
2015
We go on in this paper, in the study of the solutions of the focusing NLS equation. With a new representation given in a preceding paper, a very compact formulation without limit as a quotient of two determinants, we construct the Peregrine breather of order N=10. The explicit analytical expression of the Akhmediev's solution is completely given.
Collective coordinate approach for the dynamics of light pulses in fiber ring lasers
2014
We present an efficient variational approach for fiber lasers in which light pulses may execute complex dynamics, and we establish its validity by comparison with the numerical approach based on the generalized nonlinear Schroedinger equation.
Condensation of classical nonlinear waves
2005
We study the formation of a large-scale coherent structure (a condensate) in classical wave equations by considering the defocusing nonlinear Schr\"odinger equation as a representative model. We formulate a thermodynamic description of the condensation process by using a wave turbulence theory with ultraviolet cut-off. In 3 dimensions the equilibrium state undergoes a phase transition for sufficiently low energy density, while no transition occurs in 2 dimensions, in analogy with standard Bose-Einstein condensation in quantum systems. Numerical simulations show that the thermodynamic limit is reached for systems with $16^3$ computational modes and greater. On the basis of a modified wave tu…
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.
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…
Nonlinear excitations in a compressible quantum Heisenberg chain
2000
Abstract We investigate, both analytically and numerically, nonlinearly coupled magnetic and elastic excitations of compressible Heisenberg chains. From a shallow water wave treatment of perturbation terms, one can derive two types of coupled equations which are coupled Boussinesq and nonlinear Schrodinger (NLS) equations and coupled Boussinesq and NLS-like equations. We also simulate collisions between magnetic and elastic solitons in the compressible Heisenberg chain when a nonlinearized approach is performed to deal with the magnetic modes in the presence of harmonic as well as anharmonic interactions. Finally, from a fast Fourier transform (FFT) algorithm, the dynamical structure factor…
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…
LONG TIME DYNAMICS OF MODULATED WAVES IN A NONLINEAR DISCRETE LC TRANSMISSION LINE
2003
The long-time dynamics of modulated waves in a nonlinear LC transmission line is investigated. Considering the higher-order nonlinear Schrodinger equation, we define analytically the conditions leading to the instability of modulated waves. We show that two kinds of instabilities may develop in the network depending on the frequency range of the chosen carrier wave and on the magnitude of its initial amplitude, which is confirmed by our numerical simulations. The nonreproducibility of numerical experiments on modulated waves is also considered.
Discrete-ring vortex solitons
2010
We study analytically and numerically the existence and stability of discrete vortex solitons in the circular arrays of nonlinear optical waveguides, governed by the discrete nonlinear Schrodinger equation. Stable vortex breathers with periodically oscillating topological charge are identified and a continuous interpolating map is constructed which allows to recover trajectories of individual phase dislocations in the form of hyperbolic avoided crossings.