In this research paper, (2 + 1)-dimensional Chaffee-Infante equation, with applications in fluid dynamics, nonlinear fiber optics, coastal engineering, ion-acoustic modeling, sound waves, electromagnetic field waves, and plasma physics, is explored and analyzed to calculate is analytic exact solutions utilizing two effective exact methods named as, extended $$(\frac{G'}{G^2})$$( G ′ G 2 ) -expansion method and new (F/G)-expansion method. These techniques work wonderfully to produce exact solutions for many nonlinear problems that arise in various disciplines of scientific fields. The proposed methods are employed to extract the soliton solutions of the proposed equation. These exact methods are implemented successfully and provide many soliton solutions. The extracted soliton solutions contain hyperbolic, trigonometric and rational functions. Graphical analysis is provided using 3D surface plots and 2D contour plots in order to comprehend the physical structure of the obtained solutions.