Abstract We report the first experimental observation of spatial solitons with complex polarization states, called Poincaré (PPSs) in lead glass strongly nonlocal nonlinearity. The formations PPSs topological charge l = 1, including cylindrical elliptical-polarization soliton (CEPS) and angularly-hybrid (AHPS), were observed. showed that annular profiles distributions first-order can be remaine...

in this paper, a numerical solution procedure is presented for the forced vibration of a piezoelectric nanowire under thermo-electro-mechanical loads based on the nonlocal elasticity theory within the framework of timoshenko beam theory. using hamilton’s principle, the nonlocal governing differential equations are derived. the governing equations and the related boundary conditions are discreti...

We are concerned with the existence and form of positive solutions to a nonlinear third-order three-point nonlocal boundary-value problem on general time scales. Using Green’s functions, we prove the existence of at least one positive solution using the Guo-Krasnoselskii fixed point theorem. Due to the fact that the nonlinearity is allowed to change sign in our formulation, and the novelty of t...

The interplay between space and evolution is an important issue in population dynamics, that is particularly crucial in the emergence of polymorphism and spatial patterns. Recently, biological studies suggest that invasion and evolution are closely related. Here, we model the interplay between space and evolution starting with an individual-based approach and show the important role of paramete...

We investigate quantitative properties of nonnegative solutions u(x) ≥ 0 to the semilinear diffusion equation Lu = f(u), posed in a bounded domain Ω ⊂ R with appropriate homogeneous Dirichlet or outer boundary conditions. The operator L may belong to a quite general class of linear operators that include the standard Laplacian, the two most common definitions of the fractional Laplacian (−∆) (0...

We study cascaded quadratic soliton compressors and address the physical mechanisms that limit the compression. A nonlocal model is derived, and the nonlocal response is shown to have an additional oscillatory component in the nonstationary regime when the group-velocity mismatch (GVM) is strong. This inhibits efficient compression. Raman-like perturbations from the cascaded nonlinearity, compe...

The Schrödinger-Poisson-Xα (S-P-Xα) model is a “local one particle approximation” of the time dependent Hartree-Fock equations. It describes the time evolution of electrons in a quantum model respecting the Pauli principle in an approximate fashion which yields an effective potential that is the difference of the nonlocal Coulomb potential and the third root of the local density. We sketch the ...

In this work, based on the recently proposed (Phys. Rev. Lett. 110 (2013) 064105) continuous nonlocal nonlinear Schrödinger system with parity-time symmetric Kerr nonlinearity (PTNLSE), a numerical investigation has been carried out for two first order Peregrine solitons as the initial ansatz. Peregrine soliton, as an exact solution to the PTNLSE, evokes a very potent question: what effects doe...

Bound states of solitons, alias soliton molecules (SMs), are well known in 1D systems, while making stable bound multidimensional solitons is a challenging problem because the underlying instabilities. Here, scheme for creation (2+1)D and (3+1)D optical SMs gas cold Rydberg atoms proposed, which electromagnetically induced transparency (EIT) by control laser field. It shown that, through interp...