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

Abstract

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.

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 lump

2010 Mathematics Subject Classification:

• Generalized solutions

Disclosure statement

No potential conflict of interest was reported by the authors.

Notes

1 The moving path of the wave refers to the trajectory of the highest amplitude of the wave [20].

Additional information

Funding

This work has been supported by the National Natural Science Foundation of China under Grant Nos. 11772017, 11272023 and 11805020, by the Fund of State Key Laboratory of Information Photonics and Optical Communications (Beijing University of Posts and Telecommunications), China (IPOC: 2017ZZ05) and by the Fundamental Research Funds for the Central Universities of China under Grant No. 2011BUPTYB02. UIBE Excellent Young Scholar Project (No. 18YQ12).