Abstract
The main motivation of our article is to implement generalized bilinear differential operators to create a (3+1)-dimensional potential-Yu–Toda–Sasa–Fukuyama (YTSF) like equation linked with prime number $$p=3$$ . Specific features of lump solutions realistically localized in all directions of the (3+1)-dimensional potential-YTSF like equation is founded from bilinear closed form of it. Six free parameters are exist in the achieved lump solutions. Among them two parameters are owing to the translation invariance of the YTSF equation and the remaining parameters suit a non-zero determinant condition. Some 3D plots and several contour plots of the lump solutions with demanding choices of the existing parameters are made to show energy distribution of the lump waves and can be used to visualize the other properties of rogue wave phenomena.
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