Optical systems such as signal processors, limiters, spatial light modulators, and optical computers require large and fast optical nonlinearities. Although free carrier-induced nonlinearities in semiconductors have the picosecond speeds required for use in many applications, they were considered too weak to be practical for optical systems applications. In our work, we have demonstrated that t...

We extend retrospective cost adaptive control (RCAC) with auxiliary nonlinearities to command following for uncertain Hammerstein systems with non-monotonic input nonlinearities. We assume that only one Markov parameter of the linear plant is known and that the non-monotonic input nonlinearity is uncertain. Auxiliary nonlinearities are used within RCAC to account for the non-monotonic input non...

We theoretically investigate a driven oscillator with the superconducting inductance subject to quantum phase slips (QPS). We find uncommon nonlinearities in the proposed device: they oscillate as a function of the number of photons N with a local period of the order of √N. We prove that such nonlinearities result in multiple metastable states encompassing few photons and study oscillatory depe...

In this paper we examine whether nonlinearities in the aggregate production function can explain parameter heterogeneity in the Solow (1956) growth regressions. Nonlinearities in the production technology are introduced by replacing the linear Cobb-Douglas specification with the more general CES specification. We justify our choice of production function by showing that in the context of cross-...

An overview of recent results in the field of vortex (spinning) solitons and soliton complexes composed of several fundamental (nonspinning) solitons in twoand three-dimensional optical media with competing nonlinearities is presented. It is concluded that multidimensional solitons with intrinsic topological charge are stable provided that their internal size and power (energy) are large enough...

This paper considers the adaptive robust control of nonlinear systems in the presence of parametric uncertainties and uncertain nonlinearities. The assumption on the allowable uncertain nonlinearities is relaxed to the extent that uncertain nonlinearities are required to be bounded by some known functions multiplied by unknown but bounded time-varying disturbances only. The approach uses robust...

In a recent paper [38], Struwe considered the Cauchy problem for a class of nonlinear wave and Schrödinger equations. Under some assumptions on the nonlinearities, it was shown that uniqueness of classical solutions can be obtained in the much larger class of distribution solutions satisfying the energy inequality. As pointed out in [38], the conditions on the nonlinearities are satisfied for a...

The purpose of this paper is to derive conditions for absolute stability as well as existence of solutions for multivariable Lur’e-type feedback systems whose linear part is expressed by a descriptor system. The nonlinearities are uncertain and satisfy multivariable sector conditions, or a part of the nonlinearities satisfies a norm bounded condition. Thus, the systems can be refered to as mult...

Typically, low-order nonlinearities are much stronger than high-order nonlinearities. In this Letter, we demonstrate a procedure by which strong high-order nonlinearities can be synthesized out of low-order nonlinearities. Our procedure involves the use of the previously largely overlooked process of microscopic cascading, which results from local-field effects. We have performed an experiment ...

This paper presents a unifying view of various error nonlinearities that are used in least mean square (LMS) adaptation such as the least mean fourth (LMF) algorithm and its family and the least-mean mixed-norm algorithm. Speci cally, it is shown that the LMS algorithm and its errormodi ed variants are approximations of two recently developed optimum nonlinearities which are expressed in terms ...