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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.
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
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
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
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
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