In this paper, we study in detail the existence and stability of localized pulses in a GiererMeinhardt equation with an additional ‘slow’ nonlinearity. This system is an explicit example of a general class of singularly perturbed, two component reaction-diffusion equations that goes significantly beyond wellstudied model systems such as Gray-Scott and Gierer-Meinhardt. We investigate the existe...

In this paper, we studied the progression of shallow water waves relevant to the variable coefficient Korteweg-de Vries (vcKdV) equation. We investigated two kinds of cases: when the dispersion and nonlinearity coefficients are proportional, and when they are not linearly dependent. In the first case, it was shown that the progressive waves have some geometric structures as in the case of KdV e...

Recently, graphene sheets have shown significant potential for environmental engineering applications such as wastewater treatment. In the present work, the posbuckling response of orthotropic single-layered graphene sheet (SLGS) is investigated in a closedform analytical manner using the nonlocal theory of Eringen. Two opposite edges of the plate are subjected to normal stresses. The nonlocali...

This study deals with the stochastic dynamic behaviors of nonlinear vibration of the fluid-conveying double-walled carbon nanotubes (DWCNTs) by considering the effects of the geometric nonlinearity and the nonlinearity of van der Waals (vdW) force. Besides, the small scale effects of the nonlinear vibration of the DWCNTs are investigated by using the theory of nonlocal elasticity. Some statisti...

Experiments and analyses were performed to determine the cause of a nonlinear force-deflection response observed in four-point flexural fatigue of beams of cortical bone machined from the mid-diaphysis of the equine third metacarpus. Observable grooves which formed on the beam surface at supports and load noses were found to be the primary cause of the nonlinearity. An additional geometric nonl...