A back-propagation neural network is applied to a nonlinear self-tuning tracking problem. Traditional self-tuning adaptive control techniques can only deal with linear systems or some special nonlinear systems. The emerging back-propagation neural networks have the capability to learn arbitrary nonlinearity and show great potential for adaptive control applications. A scheme for combining back-...

We present shape-preserving self-accelerating beams of Maxwell's equations with optical nonlinearities. Such beams are exact solutions to Maxwell's equations with Kerr or saturable nonlinearity. The nonlinearity contributes to self-trapping and causes backscattering. Those effects, together with diffraction effects, work to maintain shape-preserving acceleration of the beam on a circular trajec...

In this paper, we perform a stability analysis of 2D, noncircular self-similar crystals with isotropic surface tension growing in a supercooled melt. The existence of such self-similarly growing crystals was demonstrated recently in our previous work (J. Crystal Growth 267 (2004) 703). Here, we characterize the nonlinear morphological stability of the self-similar crystals, using a new spectral...

Solitons are typically stable objects in 1D models, but their straightforward extensions to 2D and 3D settings tend be unstable. In particular, the ubiquitous nonlinear Schroedinger (NLS) equation with cubic self-focusing, creates only unstable solitons, because same gives rise critical supercritical collapse cases, respectively. This article offers, first, a review of relevant which, neverthel...