Search results for "SOLITONS"
showing 10 items of 401 documents
Tenth Peregrine breather solution of the NLS equation.
2012
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.
Three dimensional reductions of four-dimensional quasilinear systems
2017
In this paper we show that integrable four dimensional linearly degenerate equations of second order possess infinitely many three dimensional hydrodynamic reductions. Furthermore, they are equipped infinitely many conservation laws and higher commuting flows. We show that the dispersionless limits of nonlocal KdV and nonlocal NLS equations (the so-called Breaking Soliton equations introduced by O.I. Bogoyavlenski) are one and two component reductions (respectively) of one of these four dimensional linearly degenerate equations.
A numerical study of the small dispersion limit of the Korteweg-de Vries equation and asymptotic solutions
2012
Abstract We study numerically the small dispersion limit for the Korteweg–de Vries (KdV) equation u t + 6 u u x + ϵ 2 u x x x = 0 for ϵ ≪ 1 and give a quantitative comparison of the numerical solution with various asymptotic formulae for small ϵ in the whole ( x , t ) -plane. The matching of the asymptotic solutions is studied numerically.
Spiking patterns emerging from wave instabilities in a one-dimensional neural lattice.
2003
The dynamics of a one-dimensional lattice (chain) of electrically coupled neurons modeled by the FitzHugh-Nagumo excitable system with modified nonlinearity is investigated. We have found that for certain conditions the lattice exhibits a countable set of pulselike wave solutions. The analysis of homoclinic and heteroclinic bifurcations is given. Corresponding bifurcation sets have the shapes of spirals twisting to the same center. The appearance of chaotic spiking patterns emerging from wave instabilities is discussed.
Propagation and Stability of Novel Parametric Interaction Solitons
2006
International audience; We present a new multi-parameter family of analytical soliton solutions for nonlinear three-wave resonant interactions. We show the amplitude, phase-front shapes and general properties of the solitons. The stability of these novel parametric solitons is simply related to the value of their common group velocity.
2N+1 highest amplitude of the modulus of the N-th order AP breather and other 2N-2 parameters solutions to the NLS equation
2015
We construct here new deformations of the AP breather (Akhmediev-Peregrine breather) of order N (or AP N breather) with 2N −2 real parameters. Other families of quasi-rational solutions of the NLS equation are obtained. We evaluate the highest amplitude of the modulus of AP breather of order N ; we give the proof that the highest amplitude of the AP N breather is equal to 2N + 1. We get new formulas for the solutions of the NLS equation, different from these already given in previous works. New solutions for the order 8 and their deformations according to the parameters are explicitly given. We get the triangular configurations as well as isolated rings at the same time. Moreover, the appea…
PARAMETRIC SELF-TRAPPING OF OPTICAL BEAMS VIA RANDOM QUASI PHASE MATCHING IN LITHIUM TANTALATE WAVEGUIDE
2011
We report on experimental evidence of parametric spatial solitons in a lithium tantalate waveguide with randomized periodic ferroelectric poling. Two-color self-focusing via quadratic cascading overcomes the diffractive nature of both fundamental and frequency-doubled beams.
Nonlinear higher-order polariton topological insulator
2020
We address the resonant response and bistability of the exciton-polariton corner states in a higher-order nonlinear topological insulator realized with kagome arrangement of microcavity pillars. Such states are resonantly excited and exist due to the balance between pump and losses, on the one hand, and between nonlinearity and dispersion in inhomogeneous potential landscape, on the other hand, for pump energy around eigen-energies of corresponding linear localized modes. Localization of the nonlinear corner states in a higher-order topological insulator can be efficiently controlled by tuning pump energy. We link the mechanism of corner state formation with symmetry of the truncated kagome…
Supercontinuum optimization for dual-soliton based light sources using genetic algorithms in a grid platform
2014
We present a numerical strategy to design fiber based dual pulse light sources exhibiting two predefined spectral peaks in the anomalous group velocity dispersion regime. The frequency conversion is based on the soliton fission and soliton self-frequency shift occurring during super- continuum generation. The optimization process is carried out by a genetic algorithm that provides the optimum input pulse parameters: wavelength, temporal width and peak power. This algorithm is implemented in a Grid platform in order to take advantage of distributed computing. These results are useful for optical coherence tomography applications where bell-shaped pulses located in the second near-infrared wi…
Effect of a columnar defect on the shape of slow-combustion fronts
2003
We report experimental results for the behavior of slow-combustion fronts in the presence of a columnar defect with excess or reduced driving, and compare them with those of mean-field theory. We also compare them with simulation results for an analogous problem of driven flow of particles with hard-core repulsion (ASEP) and a single defect bond with a different hopping probability. The difference in the shape of the front profiles for excess vs. reduced driving in the defect, clearly demonstrates the existence of a KPZ-type of nonlinear term in the effective evolution equation for the slow-combustion fronts. We also find that slow-combustion fronts display a faceted form for large enough e…