Integrability, Similarity Reductions and New Classes of Exact Solutions for (3+1)-D Potential Yu–Toda–Sasa–Fukuyama Equation

In this investigation, the (3+1)-D potential Yu–Toda–Sasa–Fukuyama (YTSF) equation that arises in physical dynamics is studied for passing the painlevé test and obtaining many various exact solutions. The governing equation has many applications in fluid mechanics. Firstly, we applied the painlevé property for the governing equation and proved that the equation passes the painlevé test. After that, we utilized symmetry analysis to convert the governing equation to various ordinary differential equations. Subsequently, we obtained a new type of exact solutions for YTSF equation by using an Algorithm–Riccati method. The obtained solutions contained several arbitrary constants and functions that enhance the dynamic behaviors of these solutions. The obtained solutions include hyperbolic and trigonometric functions and represent kink wave, singularity wave and solitary wave solutions.