Abstract
Abstract: In the present study, two analytical approaches—the projective Riccati equation method as well as the (G^'/G,1/G)-expansion method—are employed to derive novel soliton solutions along with various exact waveforms of the nonlinear FAOM equation in fluid mechanics. The obtained solutions include bell-shaped, anti-bell, kink, anti-kink, and periodic wave profiles. A comparative analysis with previously established results is also undertaken. Furthermore, several graphical representations of the derived exact solutions have been produced with the aid of Maple software. Keywords: Nonlinear foam equation; generalized projective Riccati equation method; the (G^'/G,1/G)- expansion method.