The problem of local controllability for the semilinear plate equation with Dirichlet boundary conditions is studied. By making use of Schauder’s fixed point theorem and the inverse function theorem, we prove that this system is locally controllable under a super-linear assumption on the nonlinearity, that is, the initial states in a small neighborhood of 0 in a certain function space can be dr...

We exploit nonlinearity in NbN superconducting stripline resonators, which originates from local thermal instability, for studying stochastic resonance. As the resonators are driven into instability, small amplitude modulation (AM) signals are amplified with the aid of injected white noise. Simulation results based on the equations of motion for the system yield a good agreement with the experi...

New Constant Modulus (CM) algorithms are presented that are based on soft constraint satisfaction. The stationary points of an algorithm in this family is studied for an AR(p) channel and it is shown that Ding-type Undesirable Local Solutions (ULS) do not exist. This is due to the normalisation of the gradient vector and the soft nonlinearity used in these algorithms. Error Performance Surfaces...

The effective nondegenerate four-wave mixing (NDFM) susceptibility of graded metallic films with weak nonlinearity is exactly derived by invoking the local-field effects. It is found that the presence of gradation in metallic films can yield a broad resonant plasmon band in the optical region, which results in a large enhancement in the NDFM response and thus a large figure of merit. © 2005 Ame...

The existence of lower dimensional KAM tori is shown for a class of nearly integrable Hamiltonian systems where the second Melnikov’s conditions are relaxed, at the cost of the stronger regularity of the perturbed nonlinear term. As a consequence, it is proved that there exist many linearly stable invariant tori and thus quasi-periodic solutions for nonlinear wave equations of non-local nonline...

In this paper, we give a KAM theorem for a class of infinite dimensional nearly integrable Hamiltonian systems. The theorem can be applied to some Hamiltonian partial differential equations in higher dimensional spaces with periodic boundary conditions to construct linearly stable quasi–periodic solutions and its local Birkhoff normal form. The applications to the higher dimensional beam equati...

We consider the nonlinear Schrödinger equation in higher dimension with Dirichlet boundary conditions and with a non-local smoothing nonlinearity. We prove the existence of small amplitude periodic solutions. In the fully resonant case we find solutions which at leading order are wave packets, in the sense that they continue linear solutions with an arbitrarily large number of resonant modes. T...

In this paper we study stopping time and impulse control problems for stochastic Navier-Stokes equation. Exploiting a local monotonicity property of the nonlinearity, we establish existence and uniqueness of strong solutions in two dimensions which gives a Markov-Feller process. The variational inequality associated with the stopping time problem and the quasi-variational inequality associated ...

The propagation properties of transverse localized structures are studied experimentally and numerically, showing that their free-space behavior is determined by the features acquired during the nonlinear light-matter interaction at their origin. For a Kerr-like nonlinearity in the optical loop, localized structures show a focalization followed by the formation of a local minimum of the intensi...

We develop an averaging method for solitons of the nonlinear Schrödinger equation with a periodically varying nonlinearity coefficient, which is used to effectively describe solitons in Bose-Einstein condensates, in the context of the recently proposed technique of Feshbach resonance management. Using the derived local averaged equation, we study matter-wave bright and dark solitons and demonst...