Huxley equation is a core mathematical framework for modern biophysically based neural modeling. It is often useful to obtain a generalized solitary solution for fully understanding its physical meanings. There are many methods to solve the equation, but each method can only lead to a special solution. This paper suggests a relatively new method called the Exp-function method for this purpose. ...

Abstract In the proposed work, an improvised collocation technique with cubic B-spline as basis functions is applied to obtain numerical solution of non-linear generalized Burgers’–Huxley equation, which has application in soliton theory. this technique, posteriori corrections are made interpolant and its higher-order derivatives, leads enhancement order convergence spatial domain. The temporal...

We study the isolated periodic wave trains in a class of modified generalized Burgers–Huxley equation. The planar systems with degenerate equilibrium arising after traveling transformation are investigated. By finding certain positive definite Lyapunov functions neighborhood singular points and Hopf bifurcation points, number possible limit cycles corresponding is determined. existence equation...

In this work, an efficient numerical method for the complex solutions of nonlinear partial differential equations based on the direct algebraic approach is proposed, and tested in the case of generalized Burgers–Huxley equation ∂u ∂t + αu ∂u ∂x − ∂ u ∂x2 = βu(1− u)(u − γ) Whenα = 0, δ = 1, is reduced to the Huxley equation. The proposed scheme can be used in a wide class of nonlinear reaction–d...