<p>Laser wakefield acceleration (LWFA) is a very promising technique used to generate electron beams with high energy inside a confined physical area. It is feasible to overcome the traditional limitations on electron energy like low energy efficiency, beam divergence effect, radiation losses, low acceleration gradient, big size etc., by taking use of the nonlinear characteristics of laser plasma interaction. This study presents a comprehensive summary of the most recent advancements in using nonlinear effects to increase electron energy in laser wakefield acceleration. This work presents the formulation of a differential equation that represents the wake potential produced by LWFA in the weakly-relativistic domain inside a homogeneous plasma under dense conditions. An analytical calculation has been performed to determine the wakefield and energy gain by using the wake potential generated by a Gaussian-like sinusoidal laser pulse. This study examines the impact of laser electric field amplitude on the magnitude of the produced wakefield. An analysis of laser pulse length reveals that the highest electron energy gain may be achieved when the laser pulse length is 0.65 times the plasma wavelength. The present study aims to enhance electron energy by precise adjustment of parameters related to wakefield phenomena.</p>