In this paper, we have extended the recently introduced theory of coupled propagation of two coaxially co-propagating and mutually incoherent bright 1-D beams to coupled propagation of two 2-D (cylindrical) bright beams and investigated the propagation behavior and spatial soliton pair formation of such beams by a recently introduced simple approach. We have considered saturable form of the non...

We complete the study of [16] and [20] about the Miller algorithm. The Miller algorithm is a central step to compute the Weil, Tate and Ate pairings. The aim of this article is to analyse the weakness of the Miller algorithm when it undergoes a fault attack. We prove that the Miller algorithm is vulnerable to a fault attack which is valid in all coordinate systems, through the resolution of a n...

Spatial dark optical solitons are localized light intensity dips in the infinite constant background [1–3]. Like their bright counterparts, they propagate preserving their spatial profile. This is a result of a balance between diffraction which tends to broaden their size and nonlinearity of the medium which counteracts this process. The existence of dark spatial solitons requires the nonlinear...

When solvinglinear scattering problems, one typically first solves for the impinging wave in the absence of obstacles. Then, using the linear superposition principle, the original problem is reduced to one which involves only the scattered wave (which is driven by the values of the impinging field at the surface of the obstacles). When the original domain is unbounded, special artificial bounda...

The transient behavior of the fundamental amplitude of the photorefractive space-charge field is derived without restrictions within the band transport model. The two-wave mixing pulse excitation regime is simulated in different ranges of the main parameters, especially in the region where the nonlinear processes become important. The formation and decay of the field are analyzed, and for diffe...

We investigate left-handed (LH) travelling-wave fieldeffect transistors (TWFETs) to observe the reverse Doppler effect. Due to the nonlinearity, a TWFET can support shock fronts that can reflect incoming waves. By introducing the composite right/left-handed line structure to a TWFET, it enables to support LH waves. Because the shock front functions as a moving reflection wall to the incoming LH...

The motion of free nearby test particles relative to a stable equatorial circular geodesic orbit about a Kerr source is investigated. It is shown that the nonlinear generalized Jacobi equation can be transformed in this case to an autonomous form. Tidal dynamics beyond the critical speed c/ √ 2 is studied. We show, in particular, that a free test particle vertically launched from the circular o...

In this paper, adaptive dynamic surface control (DSC) is developed for a class of pure-feedback nonlinear systems with unknown dead zone and perturbed uncertainties using neural networks. The explosion of complexity in traditional backstepping design is avoided by utilizing dynamic surface control and introducing integral-type Lyapunov function. It is proved that the proposed design method is a...

We prove results on solvability of nonlinear elliptic partial differential systems of principle type of second order. They are consequences of existence of non-radial solutions for nonlinear partial differential systems of Poisson type. As applications to geometry, we prove the exsitence of local harmonic maps with given tangent plane at a point between any Riemannan manifolds. More generally g...

An overview is given of the interplay between symmetries, singularities and integrability and their uses in nonlinear problems arising in Mathematical Physics and Cosmology. A particularly important aspect is the role of nonlocal symmetries in deciding about integrability of complex nonlinear problems which do not apparently admit solutions in closed form. The need for a new approach to the evo...