Lump, lumpoff, rogue wave, breather wave and periodic lump solutions for a \((3+1)\)-dimensional generalized Kadomtsev-Petviashvili equation in fluid mechanics and plasma physics. (English) Zbl 1483.35166
Summary: Under investigation in this paper is a \((3+1)\)-dimensional generalized Kadomtsev-Petviashvili equation in fluid mechanics and plasma physics. With the help of symbolic computation, we obtain and discuss the influence of the perturbed effect and disturbed wave velocity along the transverse spatial coordinate on the lump, lumpoff, rogue wave, breather wave and periodic lump solutions: When the value of \(\delta_2\) decreases to \(-1\), the amplitude of the lump wave becomes smaller; When the value of \(\delta_1\) increases to 5, the location of the lump wave moves along the positive direction of the \(y\) (a transverse spatial coordinate) axis; When the value of \(\delta_2\) decreases to 0.5, the location of the stripe soliton moves along the negative direction of the \(y\) axis and the amplitude of the lump wave becomes smaller; When the value of \(\delta_2\) decreases to \(-0.4\), the amplitude of the rogue wave becomes smaller; When the value of \(\delta_1\) increases to 5, breather waves propagate along the positive \(t\) (the temporal coordinate) direction and distance between the adjacent crests becomes shorter; When the value of \(\delta_2\) decreases to \(-1\), breather waves propagate along the negative \(t\) direction and distance between the adjacent crests becomes shorter; When the value of \(\delta_2\) decreases to 0.5, periodic lump waves move along the positive direction of the \(y\) axis. Lump solutions have more parameters than those in the existing literature. Lumpoff wave is generated from the process of the interaction between the lump wave and one stripe soliton. Moving path of the lumpoff wave is investigated via the moving path of the lump wave. Besides, we derive the rogue wave, breather wave and periodic lump solutions.
MSC:
| 35Q35 | PDEs in connection with fluid mechanics |
| 35D99 | Generalized solutions to partial differential equations |
| 76X05 | Ionized gas flow in electromagnetic fields; plasmic flow |
| 82D10 | Statistical mechanics of plasmas |
Keywords:
fluid mechanics; plasma physics; \((3+1)\)-dimensional generalized Kadomtsev-Petviashvili equation; influence of the perturbed effects and disturbed wave velocities along the transverse spatial coordinates; lumpoff; breather waves; periodic lumpReferences:
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