New solitary waves and exact solutions for the fifth-order nonlinear wave equation using two integration techniques

In this paper, we discussed the enhanced Kudryashov’s and general projective Riccati equations techniques for obtaining exact solutions to the fifth-order nonlinear water wave (FONLWWE) equation. Using the enhanced Kudryashov’s method, we were able to achieve solitary wave and singular soliton solutions. Solitary-shock hybrid wave, singular soliton, and periodic wave solutions were discovered when we employed the general projective Riccati equations approach. We can say the given methods are effective and powerful for obtaining exact solutions. Our findings in this paper are critical for explaining a wide range of scientific and oceanographic applications involving ocean gravity waves and other related phenomena.