Travelling wave solutions for the generalized Burgers–Huxley equation

A positive and bounded finite element approximation of the generalized Burgers–Huxley equation

“…Numerical experiment 3 investigates the predicted a priori error estimate. A traveling wave solution of (1) for the case when β = 1 is given by [8] u(…”

The first integral method for constructing exact and explicit solutions to nonlinear evolution equations

“…The approach is currently known as the first integral method. The method has found several applications in the applied sciences (see, for instance, [21][22][23][24][25][26][27][28] and the references therein). The main idea behind the method is to construct a polynomial first integral (with polynomial coefficients) to an autonomous planar system which is equivalent to the equation to be solved.…”

Soliton-like solutions to the generalized Burgers-Huxley equation with variable coefficients

“…An interesting physical situation is when the coefficients are equal to = 1 = −1 α = 0 and δ is a constant; this case reduces the considered Eq. (3) to the so-called Newwell-Whitehead equation [22,23]. Under these conditions, ( ) can be determined explicitly following to (19) as (25) Note that, in this case, the constants θ 1 θ 2 and θ 3 in (21) will be equal to…”