Approximations of slightly nonlinear systems with linear time-invariant (LTI) models are often used in applications. Here, LTI models that are optimal approximations in the mean-square error sense are studied. It is shown that these models can be very sensitive to small nonlinearities. Furthermore, the significance of the distribution of the input process is discussed. From the examples studied...

It is demonstrated that optical solitons can propagate in a dispersive (or diffractive) medium with competing quadratic [i.e., chi((2))] and cubic [i.e., chi((3))] nonlinearities. Strong interplay between the nonlinearities leads to novel effects, in particular the following: (i) stable bright solitons can still exist in a self-defocusing (owing to cubic nonlinearity) medium supported by quadra...

We prove a nonlinear Poisson type formula for the Schrödinger group. Such a formula had been derived in a previous paper by the authors, as a consequence of the study of the asymptotic behavior of nonlinear wave operators for small data. In this note, we propose a direct proof, and extend the range allowed for the power of the nonlinearity to the set of all short range nonlinearities. Moreover,...

Most control system are influenced by static nonlinearities. It is important for an engineer to understand which is the effect of these nonlinearities. Unfortunatelly most handson laboratory can not be used for these type of experiences. In this paper it is described an ongoing project which adapts most conventional experimental setups to allow them to be used for nonlinear experiencies. In par...

We study the existence and nonexistence of classical solutions to a general Gierer-Meinhardt system with Dirichlet boundary condition. The main feature of this paper is that we are concerned with a model in which both the activator and the inhibitor have different sources given by general nonlinearities. Under some additional hypotheses and in case of pure powers in nonlinearities, regularity a...

We have studied space-charge-induced optical nonlinearities for asymmetric coupled quantum wells. By the spatial separation of heavy holes and electrons, an electrostatic potential is induced which increases the fundamental bandgap. Calculations, using the Hartree approximation, for oqtimi5ed AlGaAs structures show that a blue-shift of the band gap of 9 meV at a carrier density of 10 * cm can b...

We prove some generalizations of the first Fredholm theorem for Hammerstein operator equations in Banach spaces and study the number of their solutions using a projection like method.The linear part is assumed to be either selfadjoint or nonseladjoint while the nonlinearities are such that the corresponding map is (pseudo) A-proper. In particular, the nonlinearities can be either of monotone ty...

A mechanism for asymmetric transport which is based on parity-time-symmetric nonlinearities is presented. We show that in contrast to the case of conservative nonlinearities, an increase of the complementary conductance strength leads to a simultaneous increase of asymmetry and transmittance intensity. We experimentally demonstrate the phenomenon using a pair of coupled Van der Pol oscillators ...

In this paper‎, ‎we prove a multiplicity result for some biharmonic elliptic equation of Kirchhoff type and involving nonlinearities with critical exponential growth at infinity‎. ‎Using some variational arguments and exploiting the symmetries of the problem‎, ‎we establish a multiplicity result giving two nontrivial solutions‎.

We present a numerical method for a class of boundary value problems on the unit interval which feature a type of exponential and product nonlinearities. Also, we consider singular case. We construct a kind of spectral collocation method based on shifted Jacobi polynomials to implement this method. A number of specific numerical examples demonstrate the accuracy and the efficiency of the propos...