Lumps, solitons and stability analysis for the (3 + 1)-dimensional fractional potential-YTSF-like model in weakly dispersive medium

Abstract

Abstract In this study, the fractional (3 + 1)-dimensional potential Yu-Toda-Sasa-Fukuyama (YTSF)-like model is being investigated analytically and semi-analytically. The given model is converted into a bilinear form using the Hirota bilinear method. Which refers to the development of lump waves, collisions between lump waves and periodic waves, collisions between lump waves and single- and double-kink soliton solutions, and collisions between lump, periodic, and single- and double-kink soliton solutions. Furthermore, the Adomian technique and the modified extended Tanh function technique are applied to obtain several forms of innovative combinations for the governing dynamical fractional model. In addition, it has been confirmed that the established results are stable, and it has been helpful to validate the calculations. Moreover, multiple intriguing exact solutions are utilized to illustrate the physical nature of 3D, contour, and 2D graphs. A collection of bright, dark, periodic, rational, and elliptic function solutions are obtained for the solution.