Lump solution and its interaction to (3+1)-D potential-YTSF equation

Abstract

This paper studies the $$(3+1)$$ -dimensional potential-Yu–Toda–Sasa–Fukuyama (YTSF) equation by implementing the Hirota bilinear method. As a consequence, the Hirota bilinear method is successfully employed and acquired a type of the lump solution and five types of interaction solutions in terms of a new merge of positive quadratic functions, trigonometric functions and hyperbolic functions. All solutions have been verified back into its corresponding equation by Maple. We depicted the physical explanation of the extracted solutions with the free choice of the different parameters by plotting some 3D and 2D illustrations. Finally, we believe that the executed method is robust and efficient than other methods and the obtained solutions are trustworthy in the applied sciences.