Tanh method is utilized to find travelling solutions of second order nonlinear Telegraph equation. As a result, we attain dissimilar wave solutions. Our aim show that this most efficient and convenient approach for verdict differential equations. For calculation the software MAPLE used.

We use an unconditionally stable parallel difference scheme to solve telegraph equation. This method is based on domain decomposition concept and using asymmetric Saul’yev schemes for internal nodes of each sub-domain and alternating group implicit method for sub-domain’s interfacial nodes. This new method has several advantages such as: good parallelism, unconditional stability and better accu...

The FitzHugh-Nagumo equation provides a simple mathematical model of cardiac tissue as an excitable medium hosting spiral wave vortices. Here we present extensive numerical simulations studying long-term dynamics of knotted vortex string solutions for all torus knots up to crossing number 11. We demonstrate that FitzHugh-Nagumo evolution preserves the knot topology for all the examples presente...

Abstract. We consider nonlinear time dependent reaction diffusion systems in one space dimension that exhibit multiple pulses or multiple fronts. In an earlier paper two of the authors developed the freezing method that allows to compute a moving coordinate frame in which, for example, a traveling wave becomes stationary. In this paper we extend the method to handle multifronts and multipulses ...

Abstract—The Nagumo-Sato model is one of mathematical neuron models described by a piecewise linear difference equation. Since there is a conditional character which is discontinuous at the threshold value, the system can be classified as a hybrid dynamical system. Bifurcation phenomena are occurred by changing internal parameters and chaotic attractors are also given. The dynamical properties ...