Submitted: May 27, 2013; Accepted: Jul 5, 2013; Published: Jul 22, 2013 Abstract: In this paper, we present an algorithm called the Reduced Differential Transform Method (RDTM) to obtain approximate solutions for the Fitzhugh-Nagumo (FN) equation, Ito equation and find an exact solution to nonlinear PDE. The numerical results show that this method is a powerful tool for solving nonlinear PDEs a...

We consider the problem of initiation of a propagating wave in a one-dimensional bistable or excitable fiber. In the Zeldovich-Frank-Kamenetskii equation, also known as the Nagumo equation and Schlögl model, the key role is played by the "critical nucleus" solution whose stable manifold is the threshold surface separating initial conditions leading to the initiation of propagation and decay. An...

This paper presents a new method for solving higher order nonlinear evolution partial differential equations (NPDEs). The method combines quasilinearisation, the Chebyshev spectral collocation method, and bivariate Lagrange interpolation. In this paper, we use the method to solve several nonlinear evolution equations, such as the modified KdV-Burgers equation, highly nonlinear modified KdV equa...

In this article, we analyze traveling waves in a reaction–diffusionmechanics (RDM) system. The system consists of a modified FitzHugh–Nagumo equation, also known as the Aliev–Panfilov model, coupled bidirectionally with an elasticity equation for a deformable medium. In one direction, contraction and expansion of the elastic medium decreases and increases, respectively, the ionic currents and a...

We investigate existence and uniqueness of solutions of a McKeanVlasov evolution PDE representing the macroscopic behaviour of interacting Fitzhugh-Nagumo neurons. This equation is hypoelliptic, nonlocal and has unbounded coefficients. We prove existence of a solution to the evolution equation and non trivial stationary solutions. Moreover, we demonstrate uniqueness of the stationary solution i...

In this paper we review the existence of diierent types of travelling wave solutions u(x; t) = (x ? ct) of degenerate non-linear reaction-diiusion equations of the form u t = D(u)u x ] x + g(u) for diierent density-dependent diiusion coeecients D and kinetic part g. These include the non-linear degenerate generalized Fisher-KPP and the Nagumo equations. Also, we consider an equation whose diius...

The authors investigate the solution of a nonlinear reaction-diffusion equation connected with nonlinear waves. The equation discussed is more general than the one discussed recently by Manne, Hurd, and Kenkre (2000). The results are presented in a compact and elegant form in terms of Mittag-Leffler functions and generalized Mittag-Leffler functions, which are suitable for numerical computation...