Under special conditions an approximate wave front solution to a system of nonlinear reaction-diffusion type equations is obtained. An assumption of fast kinetics permits the system to be reformulated as a single nonlinear differential-integral equation of convolution type. If the convolution kernel has the form of a mollifier then the convolution is localized to obtain an infinite system of di...

In their proof of the stability of standing-wave solutions of nonlinear Schrödinger equations, Cazenave and Lions used the principle of concentration compactness to characterize the standing waves as solutions of a certain variational problem. In this article we first review the techniques introduced by Cazenave and Lions, and then discuss their application to solitary-wave solutions of nonloca...

By means of computerized symbolic computation and a modified extended tanhfunction method the multiple travelling wave solutions of nonlinear partial differential equations is presented and implemented in a computer algebraic system. Applying this method, we consider some of nonlinear partial differential equations of special interest in nanobiosciences and biophysics namely, the transmission l...