perturbation method

Exact Solitary-wave Solutions of the Burgers – Huxley and Bradley – Harper Equations

It is shown that the exact soliton-like solutions of nonlinear wave mechanics evolution equations can be obtained by direct perturbation method based on the solution of a linearized equation. The sought solutions are sums of the perturbation series which can be found using the requirement that the series are to be geometric. This requirement leads to the conditions for the coefficients of the equations and parameters of the sought solutions.