Abstract
Kadomtsev–Petviashvili equation is used for describing the long water wave and small amplitude surface wave with weak nonlinearity, weak dispersion, and weak perturbation in fluid mechanics. Based on the modified symbolic computation approach, the multiple rogue wave solutions of a generalized (3+1)dimensional variablecoefficient Kadomtsev–Petviashvili equation are investigated. When the variable coefficient selects different functions, the dynamic properties of the derived solutions are displayed and analyzed by different threedimensional graphics and contour graphics.
1 Introduction
With the development of the world economy, maritime safety has become an important research topic in the field of marine engineering. Strong nonlinear waves can cause nonlinear problems such as wave climbing and slamming of offshore structures, which bring great wave loads and are a huge threat to the safety of offshore structures [1]. A rogue wave is such a strong nonlinear extreme wave with remarkable characteristics such as extremely high wave height, prominent wave crest, concentrated energy, and large destructive power. The concept of rogue wave was first proposed by Draper [2] in 1965, and since then, the phenomenon of rogue waves and its influence on offshore structures have received extensive attention. People called the rogue wave “deep sea monster,” describing it like a wall of water, appearing suddenly, and then quickly disappearing without a trace. Currently, it has been found that rogue wave widely exist in various sea areas of the world, which can appear in the deep sea and offshore sea, in stormy weather and general weather, but most of them are stormy weather. Therefore, the study of rogue wave is of great significance [3,4,5].
In this work, under investigation is a generalized (3+1)dimensional variablecoefficient Kadomtsev–Petviashvili equation (vcKPe) [6]:
where
This article is organized as follows. Section 2 gives the oneorder rogue wave solution; Section 3 presents the threeorder rogue wave solution; Section 4 derives the sixorder rogue wave solution; Section 5 presents a conclusion.
2 Oneorder rogue wave solution
Under the assumption
where
Based on the modified symbolic computation approach [13,14,15], we suppose that Eq. (3) has the following solution:
where
Substituting Eqs. (4) and (5) into Eq. (2), the oneorder rogue wave solution of Eq. (1) is written as follows:
When
3 Threeorder rogue wave solution
To obtain the threeorder rogue wave solution of Eq. (1), we choose
where
Substituting Eqs. (7) and (8) into Eq. (2), the threeorder rogue wave solution of Eq. (1) is obtained as follows:
When
4 Sixorder rogue wave solution
To present the sixorder rogue wave solution of Eq. (1), we have
where
Substituting Eqs. (10) and (11) into Eq. (2), the sixorder rogue wave solution of Eq. (1) is obtained as follows:
When
5 Conclusion
In this work, a generalized (3+1)dimensional vcKPe are studied. Based on the modified symbolic computation approach and symbolic computation [16,17,18, 19,20,21, 22,23,24, 25,26,27, 28,29,30, 31,32,33, 34,35,36, 37,38,39, 40,41,42, 43,44], we obtain the multiple rogue wave solutions of the generalized (3+1)dimensional vcKPe. By selecting different functions of the variable coefficient, the dynamic properties of the derived solutions are shown in Figures 1–7. In Figure 1, we can find a rogue wave spreading. When

Funding information: The authors state no funding involved.

Author contributions: All authors have accepted responsibility for the entire content of this manuscript and approved its submission.

Conflict of interest: The authors state no conflict of interest.

Data availability statement: Data sharing not applicable to this article as no datasets were generated or analyzed during the current study.
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