Two well-known methods for the design of quasicrystal models are used to create novel nonlinear optical devices. These devices are useful for efficient three-wave mixing of several different processes, and therefore offer greater flexibility with respect to the more common periodic nonlinear photonic crystals. We demonstrate applications for polarization switching as well as multi-wavelength an...

In this work a glottal model loosely based on the Ishizaka and Flanagan model is proposed, where the number of parameters is drastically reduced. First, the glottal excitation waveform is estimated, together with the vocal tract filter parameters, using inverse filtering techniques. Then the estimated waveform is used in order to identify the nonlinear glottal model, represented by a closedloop...

The present paper extends some results recently developed for the analysis of observability in nonlinear dynamical systems. The aim of the paper is to address the problem of embedding an attractor using more than one observable. A multivariate nonlinear observability matrix is proposed which includes the monovariable nonlinear and linear observability matrices as particular cases. Using the dev...

Nonlinear theory describing the instability-induced dynamics of dark solitons in the generalized nonlinear Schrödinger equation is presented. Equations for the evolution of an unstable dark soliton, including its transformation into a stable soliton, are derived using a multiscale asymptotic technique valid near the soliton instability threshold. Results of the asymptotic theory are applied to ...

The interaction of self-localized waves with an abrupt interface is a problem of fundamental importance in many branches of physics, engineering, and applied mathematics. Waveguide optics, for instance, is dominated in an essential way by such considerations. There, the full complexity of electromagnetic propagation is conveniently reduced to an equation of the nonlinear Schrödinger (NLS) class...

The numerical approximation of the solution of the time-dependent Schrödinger equation arising in ultrafast laser dynamics is discussed. The linear electronic Schrödinger equation is reduced to a computationally tractable, lower dimensional system of nonlinear partial differential equations by the multi-configuration timedependent Hartree-Fock method (MCTDHF). This method uses an ansatz for the...

We investigate the evolution of nonlinear density perturbations by taking into account the effects of shear and angular momentum of the system. Starting from the standard spherical top hat model in which these terms are ignored, we introduce a physically motivated closure condition which specifies the dependence of these terms on δ. The modified equation can be used to model the behavior of an ...

Following the authors’ earlier work in [9, 10], we show that the nonlinear eigenvalue problem introduced in [10] can be recast in the language of bifurcation theory as a perturbation of a linearized eigenvalue problem. Solutions of this nonlinear eigenvalue problem correspond to time periodic solutions of the compressible Euler equations that exhibit the simplest possible periodic structure ide...

The KP equation, which is an integrable nonlinear evolution equation in 2 + 1, i.e., two spatial and one temporal dimensions, is a physically significant generalization of the KdV equation. The question of constructing an integrable generalization of the KP equation in 3+1, has been one of the central open problems in the field of integrability. By complexifying the independent variables of the...

A method is developed for model predictive control of nonlinear stochastic partial differential equations (PDEs) to regulate the state variance, which physically represents the roughness of a surface in a thin film growth process, to a desired level. Initially a nonlinear stochastic PDE is formulated into a system of infinite nonlinear stochastic ordinary differential equations by using Galerki...