Dynamic investigation to the generalized Yu–Toda–Sasa–Fukuyama equation using Darboux transformation

Numerous variations of cognitive challenges, such as those in fluid mechanics, plasma physics and nonlinear optics as well as in engineering and mathematics, involve nonlinear partial differential equations. In this study, we explore the (3+1)-dimensional generalized Yu–Toda–Sasa–Fukuyama (YTSF) equation with application in engineering and physical science. Three (1+1)-dimensional nonlinear partial differential equations can be acquired from the YTSF equation. Using a N-fold Darboux transformation technique of Lax pair to obtain the multi-soliton, resonant and complex soliton solutions of the equation. Also, by showing the solutions graphically, the completeness of the outcome was confirmed. The conclusions in this study might be useful for understanding the soliton solutions in mathematics and physics.