Stability analysis and solitary wave solutions for Yu Toda Sasa Fukuyama equation: Stability analysis and solitary wave solutions: S. T. Rizvi et al.

In this work, we present a detail analysis on (3+1)-dimensional Yu Toda Sasa Fukuyama (YTSF) equation. YTSF has so many applications in the description of elastic quasiplane waves in a lattice and interfacial waves in a two-layer fluid system. The YTSF equation represents the dynamics of the interface between two immiscible fluid layers of varying densities in the setting of interfacial waves in a two-layer liquid. The equation takes into account the nonlinear effects and dispersion that occur in a system where these layers may have varying velocities. Stable soliton-like structures localized waves that hold their shape while propagating can be described by the YTSF equation because of its integrability. With the aid of extended modified auxiliary equation mapping, we establish some solitary wave solutions (SWS) like various types of kink, periodic, doubly periodic, bell type, trigonometric, rational, and combined SWS, which have various applications in engineering and physical sciences. The behaviour of flaws in crystalline structures or phase transitions in materials is described by kink and anti-kink solutions. This approach gives us various types of SWS as compared to other analytical methods. We also discuss the stability analysis (SA) for our model. The SA involves examining whether the solutions to the equation, particularly SWS or other waveforms, maintain their structure over time when subjected to small perturbations. In other words, it determines whether these solutions are stable or unstable under slight changes in initial conditions or in the parameters of the system. Finally, we will provide graphical representation to the obtained solutions in various dimensions like 3D, 2D and contour plots by using mathematica with suitable values of subsequent parameters. For the first time, we use this approach for this model and our results are new and novel. [ABSTRACT FROM AUTHOR]