Abstract
This research is based on finding new soliton solutions of Mikhailov-Novikov-Wang integrable equation. Three most efficient and reliable techniques have been employed in this article for obtaining desired results. These techniques include singular manifold method, exp(−Φ(ξ))-expansion method and generalized projective Riccati equations method. The hyperbolic function solutions and trigonometric function solutions have been extracted using the proposed methods. All of the developed solutions meet the existence criterion. The numerical simulations have been carried out using 2D and 3D figures of the obtained solutions. Further, the investigation of the sensitivity behavior of the system under certain initial conditions. Taking various initial values with a suitable free parameter, the dynamic behavior has been shown via phase portraits. These portraits demonstrate that the system under discussion is not highly sensitive for these initial conditions.