We investigate a power tunable junction formed by two interacting spatial solitons self-trapped in nematic liquid crystals. By launching a counter-propagating copolarized probe we assess the guided-wave behavior induced by the solitons and demonstrate a novel all-optical switch. Varying soliton power the probe gets trapped into one or two or three guided-waves by the soliton-induced index pertu...

We predict theoretically and generate in a photorefractive crystal two-dimensional self-trapped periodic waves of different symmetries, including vortex lattices-patterns of phase dislocations with internal energy flows. We demonstrate that these nonlinear waves exist even with anisotropic nonlocal nonlinearity when the optically-induced periodic refractive index becomes highly anisotropic, and...

We investigate the propagation of a dark beam in a defocusing medium in the strong nonlinear regime. We observe for the first time a shock fan filled with noninteracting one-dimensional gray solitons that emanates from a gradient catastrophe developing around a null of the optical intensity. This scenario turns out to be very robust, persisting also when the material nonlocal response averages ...

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...

It is shown that ambipolar diffusion as a toy nonlinearity leads to very similar behaviour of large scale turbulent dynamos as full MHD. This is demonstrated using both direct simulations in a periodic box and a closure model for the magnetic correlation functions applicable to infinite space. Large scale fields develop via a nonlocal inverse cascade as described by the alpha-effect. However, b...

In this paper we are interested in propagation phenomena for nonlocal reaction-diffusion equations of the type: ∂u ∂t = J ∗ u− u+ f(x, u) t ∈ R, x ∈ R , where J is a probability density and f is a KPP nonlinearity periodic in the xvariables. Under suitable assumptions we establish the existence of pulsating fronts describing the invasion of the 0 state by an heterogeneous state. We also give a ...

It is shown that ambipolar diffusion as a toy nonlinearity leads to very similar behaviour of large scale turbulent dynamos as full MHD. This is demonstrated using both direct simulations in a periodic box and a closure model for the magnetic correlation functions applicable to infinite space. Large scale fields develop via a nonlocal inverse cascade as described by the alpha-effect. However, b...

In this paper, we study a class of nonlocal dispersion equation with monostable nonlinearity in n-dimensional space ut − J ∗ u+ u+ d(u(t, x)) = ∫ Rn fβ(y)b(u(t− τ, x− y))dy, u(s, x) = u0(s, x), s ∈ [−τ, 0], x ∈ Rn, where the nonlinear functions d(u) and b(u) possess the monostable characters like Fisher-KPP type, fβ(x) is the heat kernel, and the kernel J(x) satisfies Ĵ(ξ) = 1 − K|ξ|α + o(|ξ|...

In dimension two, we investigate a free energy and the ground state of Schrödinger–Poisson system coupled with logarithmic nonlinearity in terms underlying functional inequalities which take into account scaling invariances problem. Such can be considered as nonlinear Schrödinger equation cubic but nonlocal Poisson nonlinearity, local nonlinearity. Both cases repulsive attractive forces are con...