Abstract
In this manuscript, with the successfully implementation of three mathematical methods, several types of exact and solitary wave solutions of the (2+1)-dimensional Boiti-Leon-Pempinelli (BLP) and (2+1)-dimensional of Boiti-Leon-Manna-Pempinelli (BLMP) equations are constructed. These schemes, namely called modified extended auxiliary mapping method, ameliorated form of simple equation and modified F-expansion. By transmission, the diverse values to the parameters, variants wave results are derived from exact peregrinating wave solution. Some solutions have been exemplified by graphical to understand the physical deportment of the BLP and BLMP wave 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 quandaries.