Search results for "equation"
showing 10 items of 4219 documents
Propagation d'informations le long d'une ligne de transmission non linéaire structurée en super réseau et simulant un neurone myélinisé
2019
Non-linear systems are almostly described by partial differential equations that characterize them. We have some systems such as the chain of coupled pebdelums, the protein chain comprising molecules with hydrogen bonds, atomic lattice, and so on .These systems are most often characterized by anharmonic inter particulate interactions and and then immersed in deformable potential substrates. In addition to nonlinearity and dispersion, these other phenomena namely anharmonicity and deformability are responsible for certain properties of propagation of solitary waves such as (compactons, kinks and anti-kinks, peackons, ...etc) and also the ability of the systems to transmit a signal . We used …
A Symplectic Kovacic's Algorithm in Dimension 4
2018
Let $L$ be a $4$th order differential operator with coefficients in $\mathbb{K}(z)$, with $\mathbb{K}$ a computable algebraically closed field. The operator $L$ is called symplectic when up to rational gauge transformation, the fundamental matrix of solutions $X$ satisfies $X^t J X=J$ where $J$ is the standard symplectic matrix. It is called projectively symplectic when it is projectively equivalent to a symplectic operator. We design an algorithm to test if $L$ is projectively symplectic. Furthermore, based on Kovacic's algorithm, we design an algorithm that computes Liouvillian solutions of projectively symplectic operators of order $4$. Moreover, using Klein's Theorem, algebraic solution…
Multi-rogue solutions to the focusing NLS equation
2010
The study of rogue waves is a booming topic mainly in oceanography but also in other fields. In this thesis I construct via Darboux transform a multi-parametric family of smooth quasi-rational solutions of the nonlinear Schödinger equation that present a behavior of rogue waves. For a general choice of parameters the second-order solutions give a model of "three sisters" (three higher than expected waves in a row) while for a particular choice of parameters we obtain the solutions given by Akhmediev et al. in a serie of articles in 2009. Then these solutions allow me to construct rational solutions of the KP-I equation that describe waves in shallow water.
Multi-parametric families solutions to the Burgers equation
2021
We construct 2N real parameter solutions to the Burgers' equation in terms of determinant of order N and we call these solutions, N order solutions. We deduce general expressions of these solutions in terms of exponentials and study the patterns of these solutions in functions of the parameters for N = 1 until N = 4.
Cut-off method for endogeny of recursive tree processes
2016
Given a solution to a recursive distributional equation, a natural (and non-trivial) question is whether the corresponding recursive tree process is endogenous. That is, whether the random environment almost surely defines the tree process. We propose a new method of proving endogeny, which applies to various processes. As explicit examples, we establish endogeny of the random metrics on non-pivotal hierarchical graphs defined by multiplicative cascades and of mean-field optimization problems as the mean-field matching and travelling salesman problems in pseudo-dimension q>1.
On Einstein bilinear form
2012
From physical motivations and from geometrical interpretations of the Einstein equations, we give a justi cation of the non-triviality and non-degeneracy of Einstein bilinear form introduced in [1].
On the analytical expression of the multicompacton and some exact compact solutions of a nonlinear diffusive Burgers’type equation
2018
International audience; We consider the nonlinear diffusive Burgers' equation as a model equation for signals propagation on the nonlinear electrical transmission line with intersite nonlinearities. By applying the extend sine-cosine method and using an appropriate modification of the Double-Exp function method, we successfully derived on one hand the exact analytical solutions of two types of solitary waves with strictly finite extension or compact support: kinks and pulses, and on the other hand the exact solution for two interacting pulse solitary waves with compact support. These analytical results indicate that the speed of the pulse compactons doesn't depends explicitly on the pulse a…
Theoretical principles of near-field optical microscopies and spectroscopies
2000
International audience; This paper deals with the principles of detection of optical signals near a surface in a manner permitting the mapping of the distribution of the fields close to various kinds of illuminated samples. We begin with a discussion of the main physical properties of the optical fields near a surface in the absence of any probe tip. This mainly concerns phenomena involving evanescent waves for which the local decay lengths are governed not only by the sizes but also by the intrinsic properties of the surface structures. The interpretation of the detection process is reviewed on the basis of a discussion about the possibility of establishing direct comparisons between exper…
All-fibered high-quality low duty-cycle 160-GHz femtosecond pulse source
2008
International audience; In this paper, we report the experimental demonstration of an all-optical fiber-based 160-GHz femtosecond pulse source exhibiting a duty cycle as low as 1/17. The 380-fs wellseparated Gaussian pulses are generated thanks to the strong temporal compression of an initial beat-signal propagating into three distinct segments of optical fiber. Experimental results are supported by numerical simulations based on the generalized nonlinear Schrödinger equation. (© 2008 by Astro Ltd., Published exclusively by WILEY-VCH Verlag GmbH & Co. KGaA)
Quasi-phase-matched third harmonic generation in optical fibers using refractive-index gratings
2011
International audience; The purpose of this work is to demonstrate the quasi-phase-matching of third harmonic generation process in optical fibers using refractive-index gratings. We compare conversion efficiency calculated with analytical coupled modes theory and numerical approach employing system of coupled generalized nonlinear Schrödinger equation. Moreover, we show that introducing the phase matching condition that takes into account the nonlinear contribution to propagation constants significantly increases the conversion efficiency by several orders of magnitude. Finally we optimize the grating constant to maximize conversion efficiency.