In this paper, we developed the parametric estimation and the self-tuning control problem of the nonlinear systems which are described by discrete-time nonlinear mathematical models, with unknown, time-varying parameters, and operative in a stochastic environment. The parametric estimation is realized by using the prediction error method and the recursive least squares techniques. The self-tuni...

In this paper, the localized TM surface waves of a nonlinear self-focusingleft-handed slab sandwiched between a uniform medium and a one-dimensionalphotonic crystal (1D PC) is analytically investigated. Our method is based on the firstintegral of the nonlinear Maxwell's equations. For the TM surface waves, the presenceof two electric field components makes the analysis difficult. Therefore, we ...

A function is called a self-similar solution of an evolution equation if its value at a given time t0 (e.g. at t0 = 1 ) it sufficient to calculate this function for all other values of time t > 0 via so-called self-similar transformation. Self-similar solutions have always played in important role in the study of properties of other solutions to linear and nonlinear evolution equations. Very of...

We propose a new type of traveling wave pattern, one that can adapt to the size of physical system in which it is embedded. Such a system arises when the initial state has an instability that extends down to zero wavevector, connecting at that point to two symmetry modes of the underlying dynamical system. The Min system of proteins in E. coli is such as system with the symmetry emerging from t...

We discuss duality invariant interactions between electromagnetic fields and matter. The case of scalar fields is treated in some detail. ∗Contribution to the memorial volume for D.V. Volkov. †This work was supported in part by the Director, Office of Energy Research, Office of High Energy and Nuclear Physics, Division of High Energy Physics of the U.S. Department of Energy under Contract DE-AC...

We demonstrate theoretically and experimentally that optical beams are self-focused and self-trapped upon initiating photopolymerization. This unique nonlinear optical phenomenon is dependent on the optical exposure and produces permanent index-of-refraction changes larger than 0.04. The resulting nonlinear wave equation is shown to be nonlocal in time and displays self-trapped solutions only f...