Search results for "Nonlinear"

Verifications of Primal Energy Identities for Variational Problems with Obstacles

2018

We discuss error identities for two classes of free boundary problems generated by obstacles. The identities suggest true forms of the respective error measures which consist of two parts: standard energy norm and a certain nonlinear measure. The latter measure controls (in a weak sense) approximation of free boundaries. Numerical tests confirm sharpness of error identities and show that in different examples one or another part of the error measure may be dominant.

Nonlinear coefficient measurement in highly dispersive fibers

2018

We present a novel approach for measuring nonlinear coefficients in fibers with significant pulse broadening. We perform a proof-of-concept demonstration for 200-m-long polarization-maintaining and single-mode fibers pumped at 1060 nm with ps pulses.

All-fiber based chaotic polarization scrambler

2014

We present a fiber-based polarization scrambler founded on the nonlinear interaction between a signal and its backward replica generated and amplified by a reflective loop. The output polarization dynamic turns out to be chaotic.

Refinement of the Dispersion Equations of the Nonlinear Biaxial Crystals KTiOAsO/sub 4/, RbTiOAsO/sub 4/ and CsTiOAsO/sub 4/. Method and Measurements

2005

Robust finite-time fuzzy H∞ control for uncertain time-delay systems with stochastic jumps

2014

Abstract This paper investigates the problem of robust finite-time H ∞ control for a class of uncertain discrete-time Markovian jump nonlinear systems with time-delays represented by Takagi–Sugeno (T–S) model. Initially, the concepts of stochastic finite-time boundedness and stochastic finite-time H ∞ stabilization are presented. Then, by using stochastic Lyapunov–Krasovskii functional approach, sufficient conditions are derived such that the resulting close-loop system is stochastically finite-time bounded and satisfies a prescribed H ∞ disturbance attenuation level in a given finite-time interval. Furthermore, sufficient criteria on stochastic finite-time H ∞ stabilization using a fuzzy s…

Oscillation of second-order nonlinear differential equations with damping

2014

Abstract We study oscillatory properties of solutions to a class of nonlinear second-order differential equations with a nonlinear damping. New oscillation criteria extend those reported in [ROGOVCHENKO, Yu. V.—TUNCAY, F.: Oscillation criteria for second-order nonlinear differential equations with damping, Nonlinear Anal. 69 (2008), 208–221] and improve a number of related results.

Infinitely many solutions for a perturbed nonlinear Navier boundary value problem involving the -biharmonic

2012

By using critical point theory, we establish the existence of infinitely many weak solutions for a class of elliptic Navier boundary value problems depending on two parameters and involving the p-biharmonic operator. © 2012 Elsevier Ltd. All rights reserved.

Kleine periodische L�sungen bei nichtlinearen stark-elliptischen Systemen von partiellen Differentialgleichungen I

1971

Strongly elliptic systems of nonlinear partial differential equations are considered in the case when the derivatives of the solutions occuring in the nonlinear terms have the same order as those in the linear principal part. The existence of periodic solutions for such systems is investigated. It is shown that this problem can be reduced to the study of algebraic bifurcation equations, whose small solutions correspond to the classical solutions of the given problem. A discussion of the bifurcation equations will be given in a forthcoming paper.

Laplace’s Method of Integration in the Path Integral Approach for the Probabilistic Response of Nonlinear Systems

2020

In this paper the response of nonlinear systems under stationary Gaussian white noise excitation is studied. The Path Integral (PI) approach, generally employed for evaluating the response Probability Density Function (PDF) of systems in short time steps based on the Chapman-Kolmogorov equation, is here used in conjunction with the Laplace’s method of integration. This yields an approximate analytical solution of the integral involved in the Chapman-Kolmogorov equation. Further, in this manner the repetitive integrations, generally required in the conventional numerical implementation of the procedure, can be circumvented. Application to a nonlinear system is considered, and pertinent compa…

Path integral method for first-passage probability determination of nonlinear systems under levy white noise

2015

In this paper the problem of the first-passage probabilities determination of nonlinear systems under alpha-stable Lévy white noises is addressed. Based on the properties of alpha-stable random variables and processes, the Path Integral method is extended to deal with nonlinear systems driven by Lévy white noises with a generic value of the stability index alpha. Furthermore, the determination of reliability functions and first-passage time probability density functions is handled step-by-step through a modification of the Path Integral technique. Comparison with pertinent Monte Carlo simulation reveals the excellent accuracy of the proposed method.