Fission and fusion solitons, and some interaction solutions for the (3+1)-dimensional kadomtsev-petviashvili-yu-toda-sasa-fukuyama equation

Abstract Employing Hirota’s bilinear method, this investigation systematically derives multi-soliton solutions for the (3+1)-dimensional Kadomtsev-Petviashvili-Yu-Toda-Sasa-Fukuyama (KP-YTSF) equation. The introduction of innovative constraint conditions has enabled, for the first time, the observation of fission-fusion phenomena in Y-type solitons within this system. Theoretical analysis reveals that modification of these constraints induces two fundamentally distinct interaction mechanisms: (i) nonlinear coupling between Y-type solitons and single solitons, and (ii) resonant interactions between Y-type solitons and lump waves. Through advanced test function methodology, we have successfully constructed several novel analytical solutions including kink breather soliton, one soliton and lump interaction solution, and intricate interference wave solution. The development of spatiotemporal evolution models coupled with dynamic density field visualization systems has provided comprehensive characterization of the solutions’ kinetic evolution properties. By combining theoretical analysis with image-based analysis, we have gained deep insights into both the mathematical nature and fundamental physical mechanisms of these nonlinear solutions.