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We present a general method based on nonlinear response theory to obtain effective interactions between ions in an electron gas which can also be applied to other systems where an adiabatic separation of time-scales is possible. Nonlinear…
This note addresses the output synchronization problem of incrementally output-feedback passive nonlinear systems in the presence of exogenous disturbances. Two kinds of distributed controllers are proposed; one placed at the nodes and the…
The q-deformation of harmonic oscillators is shown to lead to q-nonlinear vibrations. The examples of q-nonlinearized wave equation and Schr\"odinger equation are considered. The procedure is generalized to broader class of nonlinearities…
Predictor-based stabilization results are provided for nonlinear systems with input delays and a compact absorbing set. The control scheme consists of an inter-sample predictor, a global observer, an approximate predictor, and a nominal…
We consider a nonlinear model for electrical conduction in biological tissues. The nonlinearity appears in the interface condition prescribed on the cell membrane. The purpose of this paper is proving asymptotic convergence for large times…
An integrable model for SU($\nu$) electrons with inverse-square interaction is studied for the system with confining harmonic potential. We develop a new description of the spectrum based on the {\it renormalized harmonic-oscillators} which…
The paper summarizes elements of theories and computational methods that we have constructed and applied over the years for the nonperturbative solution of many electron problems, in the absence or presence of strong external fields,…
Optical chirality has been recently suggested to complement the physically relevant conserved quantities of the well-known Maxwell's equations. This time-even pseudoscalar is expected to provide further insight in polarization phenomena of…
In this work, we investigate the synchronization in oscillators with conjugate coupling in which oscillators interact via dissimilar variables. The synchronous dynamics and its stability are investigated theoretically and numerically. We…
A new simulation technique to obtain the synchronized steady-state solutions existing in coupled oscillator systems is presented. The technique departs from a semi-analytical formulation presented in previous works. It extends the model of…
In this paper, we prove the nonlinear stability under localized perturbations of spectrally stable time-periodic source defects of reaction-diffusion systems. Consisting of a core that emits periodic wave trains to each side, source defects…
We present an analytical approach to the theory of nonlinear propagation in gases of femtosecond optical pulses with broad-band spectrum . The vector character of the nonlinear third-order polarization of the electrical field in air is…
We consider the formation and stability of the vibronic polaron arising in a degenerate or nearly degenerate electronic system coupled to an appropriate vibrational mode. We define the electron-phonon coupling as a mixing of the electronic…
Circumventing the reciprocity invariance has posed an interesting challenge in the design of modern devices for wave engineering. In passive devices, operating the device in the nonlinear response regime is a common means for realizing…
This \textquoteleft research-survey' is meant for beginners in the studies of integrable systems. Here we outline some analytical methods for dealing with a class of nonlinear partial differential equations. We pay special attention to…
We present a general formalism for the construction of thermodynamically consistent stochastic models of non-linear electronic circuits. The devices constituting the circuit can have arbitrary I-V curves and may include tunnel junctions,…
We develop a method for extracting the steady nonequilibrium current from studies of driven isolated systems, applying it to the model of one-dimensional Mott insulator at high temperatures. While in the nonintegrable model the…
We show that a laser pulse can always be found that induces a desired optical response from an arbitrary dynamical system. As illustrations, driving fields are computed to induce the same optical response from a variety of distinct systems…
This work represents a first contribution on the problem of boundary stabilization for the phase field system of Cahn-Hilliard type, which models the phase separation in a binary mixture. The feedback controller we design here is with…
In this article a modified Levenberg-Marquardt method coupled with a Kaczmarz strategy for obtaining stable solutions of nonlinear systems of ill-posed operator equations is investigated. We show that the proposed method is a convergent…