In this paper we analyze a nonlocal reaction-diffusion model which arises from the modeling of competition of phytoplankton species with incomplete mixing in a water column. The nonlocal nonlinearity in the model describes the light limitation for the growth of the phytoplankton species. We first consider the single-species case and obtain a complete description of the longtime dynamical behavi...

We consider a family of sixth-order Boussinesq equations in one space dimension with an arbitrary nonlinearity. The equation was originally derived for one-dimensional lattice model considering higher order effects, and later it re-derived the context nonlinear nonlocal elasticity. In sense wave propagation solids, nonlinearity function is connected stress-strain relation physical model. Consid...

We consider diffusive nonlinear systems with nonlocal two-points coupling, generally induced by misalignment in optical feedback. We expand the stability analysis in F. Papoff and R. Zambrini [Phys. Rev. Lett. 94, 243903 (2005)] to determine convective and absolute thresholds. Nonlocality leads to different effects in comparison to well-known problems with drift, as the existence of opposite ph...

We study the existence and multiplicity of positive solutions a Riemann-Liouville fractional differential equation with r-Laplacian operator singular nonnegative nonlinearity dependent on integrals, subject to nonlocal boundary conditions containing various derivatives Riemann-Stieltjes integrals. use Guo–Krasnosel’skii fixed point theorem in proof our main results.

In the present work, effect of von Karman geometric nonlinearity on the vibration characteristics of a Y-shaped single walled carbon nanotube (Y-SWCNT) conveying viscose fluid is investigated based on Euler Bernoulli beam (EBB) model. The Y-SWCNT is also subjected to a longitudinal magnetic field which produces Lorentz force in transverse direction. In order to consider the small scale effects,...

In the present study, nonlinear vibration of coupled carbon nanotubes (CNTs) in presence of surface effect is investigated based on nonlocal Euler-Bernoulli beam (EBB) theory. CNTs are embedded in a visco-elastic medium and placed in the uniform longitudinal magnetic field. Using von Kármán geometric nonlinearity and Hamilton’s principle, the nonlinear higher order governing equations are deriv...

We consider the effects of varying dispersion and nonlinearity on the stability of periodic traveling wave solutions of nonlinear PDEs of KdV type, including generalized KdV and Benjamin–Ono equations. In this investigation, we consider the spectral stability of such solutions that arise as small perturbations of an equilibrium state. A key feature of our analysis is the development of a nonloc...