The present paper studies the novel generalized (G'/G)-expansion technique to two nonlinear evolution equations: The (2 + 1)-dimensional Konopelchenko-Dubrovsky (KD) equation and the (2 + 1)-dimensional Kadomtsev-Petviashvili (KP) equation and acquires some new exact answers. The secured answers include a particular variety of solitary wave solutions, such as periodic, compaction, cuspon, kink, soliton, a bright periodic wave, Bell shape soliton, dark periodic wave and various kinds of soliton of the studied equation are achieved. These new particular kinds of solitary wave solutions will improve the earlier solutions and help us understand the physical meaning further and interpret the nonlinear generation of nonlinear wave equations of fluid in an elastic tube and liquid, including small bubbles and turbulence and the acoustic dust waves in dusty plasmas. Additionally, the studied approach could also be employed to obtain exact wave solutions for the other nonlinear evolution equations in applied sciences. (c) 2020 The Authors. Published by Elsevier B.V. on behalf of King Saud University. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).