Dynamics of abundant solutions to the \((3 + 1)\)-dimensional generalized yu-Toda-Sasa-Fukuyama equation. (English) Zbl 1436.35066
Summary: With the aid of the direct bilinear method, the formula of \(N\)-soliton solution to the generalized \((3 + 1)\)-dimensional Yu-Toda-Sasa-Fukuyama (gYTSF) equation is succinctly obtained. By means of long-wave limit method on \(2 M\)-soliton solutions under special parameter constraints, \(M\)-order lumps can be successfully constructed. Furthermore, the propagation orbit, velocity and extremum of the \(1\)-order lump solutions on \((x,y)\) plane are studied in detail. Finally, we investigate three types of hybrid solutions, which describe interaction between breathers and solitons, or between lumps and solitons or breathers. These collisions are elastic, which do not lead any changes of amplitudes, velocities and shapes of the solitons, breathers and lumps after interaction.
MSC:
| 35C08 | Soliton solutions |
| 35C05 | Solutions to PDEs in closed form |
| 35G25 | Initial value problems for nonlinear higher-order PDEs |
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