We consider traveling wave solutions to spatially discrete reaction-diiusion equations with nonlocal variable diiusion and bistable nonlinearities. For the case of spatially periodic diiusion we obtain analytic solutions for the traveling wave problem using a piecewise linear nonlinearity. The formula for the wave forms is implicitly deened in the general periodic case and we provide an explici...

Structured plasmonic metals are widely employed for achieving nonlinear functionalities at the nanoscale due to their ability to confine and enhance electromagnetic fields and strong, inherent nonlinearity. Optical nonlinearities in centrosymmetric metals are dominated by conduction electron dynamics, which at the nanoscale can be significantly affected by the nonlocal effects. Here we show tha...

We introduce a one-dimensional phenomenological model of a nonlocal medium featuring focusing cubic and defocusing quintic nonlocal optical nonlinearities. By means of numerical methods, we find families of solitons of two types, even-parity (fundamental) and dipole-mode (odd-parity) ones. Stability of the solitons is explored by means of computation of eigenvalues associated with modes of smal...

Nonlinear bending of shear deformable nanobeams subject to a temperature field is investigated in this paper based on von Kármán type nonlinearity and nonlocal elasticity theory. By using the variational principle approach, new higher-order governing differential equations and the corresponding higher-order boundary conditions both in the transverse and axial directions are derived and discusse...

We study the existence of stationary solutions for a nonlocal version of the FisherKolmogorov-Petrovskii-Piscounov (FKPP) equation. The main motivation is a recent study by Berestycki et al. [Nonlinearity 22 (2009), pp. 2813–2844] where the nonlocal FKPP equation has been studied and it was shown for the spatial domain R and sufficiently small nonlocality that there are only two bounded non-neg...

The paper derives stationary optical solitons with nonlinear chromatic dispersion. A nonlocal form of nonlinearity and quintuple power–law are considered. Kudryashov’s integration scheme enables to retrieve such solitons. plethora come this algorithm.

Nonlinear vibration of a fluid-filled single walled carbon nanotube (SWCNT) with simply supported ends is investigated in this paper based on Von-Karman’s geometric nonlinearity and the simplified Donnell’s shell theory. The effects of the small scales are considered by using the nonlocal theory and the Galerkin's procedure is used to discretize partial differential equations of the governing i...