Novel solitary and resonant multi-soliton solutions to the (3 + 1)-dimensional potential-YTSF equation

In this study, the (3 + 1)-dimensional potential-Yu–Toda–Sasa–Fukuyama equation arising from the (3 + 1)-dimensional Kadomtsev–Petviashvili equation is investigated in detail by using two powerful approaches. First, the generalized resonant multi-soliton solution is generated via the simplified linear superposition principle. Second, after applying the simplest equation method, the generalized single solitary solution is extracted. The results show that the obtained solutions are perfect. The physical explanation of the obtained solutions is depicted in various 3D and 2D figures, which are used to illustrate that the interactions of resonant multi-soliton waves are inelastic. Ultimately, the study reveals that the inelastic interactions can be determined by the sign of the wave related number [Formula: see text].

Rational Solutions and Lump Solutions of the Potential YTSF Equation

By using of the bilinear form, rational solutions and lump solutions of the potential Yu–Toda–Sasa–Fukuyama (YTSF) equation are derived. Dynamics of the fundamental lump solution, n1-order lump solutions, and N-lump solutions are studied for some special cases. We also find some interaction behaviours of solitary waves and one lump of rational solutions.