On solutions of the Newell–Whitehead–Segel equation and Zeldovich equation

In this study, we present new solutions of Newel–Whitehead–Segel and Zeldovich equations via the new extended direct algebraic method (EDAM) by taking the special values to involved parameters in the method. The novel exact and soliton solutions are extracted in form of generalized trigonometric and hyperbolic functions. These acquired results reveal the supremacy of the new EDAM. For more illustration of our retrieved solutions, some distinct kinds of 2D and 3D graphs are presented.