Abstract
In this manuscript, with the prosperously implementation of two mathematical techniques, several types solitary waves solution of the micro-structured solids wave and the Lax' fifth-order (Lax5) equations are successfully and investigated with the aid of the mathematical software of Mathematica. These schemes namely called ameliorated form of simple equation and modified F-expansion methods. By substituting the diverse values to the parameters, variants wave results are discovered from exact peregrinating wave solution. Some solutions have been exemplified by graphical to understand the physical phenomena of the micro-structured solids wave and the Lax' fifth-order (Lax5) models. The accomplished solutions seem with all essential constraint conditions, which are obligatory for them to subsist. Hence our techniques via fortification of symbolic computations provide an active and potent mathematical implement for solving diverse benevolent nonlinear wave problems.