Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userChaotification via Higher-order Nonlinear Schrodinger Equations for Secured Communication
55
0
0.0
(
0
)
Ask ChatGPT about the research
No Arabic abstract
Higher-order nonlinear Schrodinger(HNLS) equation which can be used to describe the propagation of short light pulses in the optical fibers, is studied in this paper. Using the phase plane analysis, HNLS equation is reduced into the equivalent dynamical system, the periodicity of such system is obtained with the phase projections and power spectra given. By means of the time-delay feedback method, with the original dynamical system rewritten, we construct a single-input single-output system, and propose a chaotic system based on the chaotification of HNLS. Numerical studies have been conducted on such system. Chaotic motions with different time delays are displayed. Power spectra of such chaotic motions are calculated. Lyapunov exponents are given to corroborate that those motions are indeed chaotic.
rate research
Read More
Coupled nonlinear Schrodinger equations, governing the propagation of envelopes of electromagnetic waves in birefringent optical fibers, are studied in this paper for their potential applications in the secured optical communication. Periodicity and integrability of the CNLS equations are obtained via the phase-plane analysis. With the time-delay and perturbations introduced, CNLS equations are chaotified and a chaotic system is proposed. Numerical and analytical methods are conducted on such system: (I) Phase projections are given and the final chaotic states can be observed. (II) Power spectra and the largest Lyapunov exponents are calculated to corroborate that those motions are indeed chaotic.
The well-known Greens function method has been recently generalized to nonlinear second order differential equations. In this paper we study possibilities of exact Greens function solutions of nonlinear differential equations of higher order. We show that, if the nonlinear term satisfies a generalized homogeneity property, then the nonlinear Greens function can be represented in terms of the homogeneous solution. Specific examples and a numerical error analysis support the advantage of the method. We show how, for the Bousinesq and Kortweg-de Vries equations, we are forced to introduce higher order Green functions to obtain the solution to the inhomogeneous equation. The method proves to work also in this case supporting our generalization that yields a closed form solution to a large class of nonlinear differential equations, providing also a formula easily amenable to numerical evaluation.
We obtain novel nonlinear Schr{o}dinger-Pauli equations through a formal non-relativistic limit of appropriately constructed nonlinear Dirac equations. This procedure automatically provides a physical regularisation of potential singularities brought forward by the nonlinear terms and suggests how to regularise previous equations studied in the literature. The enhancement of contributions coming from the regularised singularities suggests that the obtained equations might be useful for future precision tests of quantum nonlinearity.
We study the formation of extreme events in incoherent systems described by envelope equations, such as the Nonliner Schrodinger equation. We derive an identity that relates the evolution of the kurtosis (a measure of the relevance of the tails in a probability density function) of the wave amplitude to the rate of change of the width of the Fourier spectrum of the wave field. The result is exact for all dispersive systems characterized by a nonlinear term of the form of the one contained in the Nonlinear Schrodinger equation. Numerical simulations are also performed to confirm our findings. Our work sheds some light on the origin of rogue waves in incoherent dispersive nonlinear media ruled by local cubic nonlinearity.
We consider the small time semi-classical limit for nonlinear Schrodinger equations with defocusing, smooth, nonlinearity. For a super-cubic nonlinearity, the limiting system is not directly hyperbolic, due to the presence of vacuum. To overcome this issue, we introduce new unknown functions, which are defined nonlinearly in terms of the wave function itself. This approach provides a local version of the modulated energy functional introduced by Y.Brenier. The system we obtain is hyperbolic symmetric, and the justification of WKB analysis follows.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
