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In this paper, we examine the solitary wave solutions of the generalised (2 + 1) extended Kadomtsev–Petviashvili (eKP) equation, which is used as model for the surface waves and internal waves in straits or channels and describes the dynamics of nonlinear waves in plasma physics and fluid dynamics. We secure distinct soliton solutions by employing two amelioration methodologies, namely the improved F -expansion method and the new Kudryashov method. These methods explore several unique forms of solitary wave solutions, including dark, rational, singular, periodic, and exponential ones. In order to illustrate propagation of some reported wave solutions, the graphs associated with these solutions are presented by choosing appropriate parametric values in 2D, 3D, contour, and density plots with the use of the symbolic software Mathematica 13.0. The presented solutions realize very significant fact for investigation the qualitative interpretations for various phenomena in our nature. The computed solutions revealed that the applied methods are influential, efficious and skilful and can be a best way to handle other higher order nonlinear evolution equations. [ABSTRACT FROM AUTHOR]

In this study, we investigate the fractional coupled nonlinear Schrödinger equation (FCNLSE) of Manakov type, which has numerous applications in different fields of physics, such as optics and plasma physics. In this study, we employ two different analytical methods, namely the auxiliary equation method (AEM) and the improved F -expansion method, to construct novel analytic exact solitary wave solutions, encompassing trigonometric, hyperbolic, and exponential functions. These solutions include solitary wave solutions dark, bright, combo, singular, rational form solutions, and periodic wave solutions. Additionally, using the characterizations of the Hamiltonian system, the stability property of the discovered soliton wave solutions is examined. We have also illustrated the sensitivity analysis for the modified dynamic structural system using different initial conditions. In order to illustrate various physical properties of wave structures, the well-furnished results are finally demonstrated in various 3D, 2D, contour, and density profiles. This work's findings highlight the significance of researching diverse nonlinear wave phenomena in physics and nonlinear optics by demonstrating how crucial it is to comprehend the physical meaning and behavior of the examined equation. The procedures used are capable, effective, and succinct enough to make it possible for further research. • A physical model nonlinear Manakov system and its sensitivity analysis are considered. • Construction of novel analytic exact solitary wave solutions is studied. • Stability property of the discovered soliton wave solutions is examined. • Well-furnished results are demonstrated in various 3D, 2D, contour, and density profiles. [ABSTRACT FROM AUTHOR]