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Characteristics of solitary waves, quasiperiodic solutions, homoclinic breather solutions and rogue waves in the generalized variable-coefficient forced Kadomtsev–Petviashvili equation

School of Mathematics and Institute of Mathematical Physics, China University of Mining and Technology, Xuzhou 221116, China

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Shou-Fu Tian

http://orcid.org/0000-0003-0888-777X

School of Mathematics and Institute of Mathematical Physics, China University of Mining and Technology, Xuzhou 221116, China

E-mail Address: sftian@cumt.edu.cn

Corresponding authors.

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Min-Jie Dong

School of Mathematics and Institute of Mathematical Physics, China University of Mining and Technology, Xuzhou 221116, China

School of Naval Architecture, State Key Laboratory of Structural Analysis for Industrial Equipment, Dalian University of Technology, Dalian 116024, China

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, and

Li Zou

School of Naval Architecture, State Key Laboratory of Structural Analysis for Industrial Equipment, Dalian University of Technology, Dalian 116024, China

Collaborative Innovation Center for Advanced Ship and Deep-Sea Exploration, Shanghai 200240, China

E-mail Address: zoulidut@126.com

Corresponding authors.

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https://doi.org/10.1142/S021798491750350XCited by:2 (Source: Crossref)

Abstract

In this paper, the generalized variable-coefficient forced Kadomtsev–Petviashvili (gvcfKP) equation is investigated, which can be used to characterize the water waves of long wavelength relating to nonlinear restoring forces. Using a dependent variable transformation and combining the Bell’s polynomials, we accurately derive the bilinear expression for the gvcfKP equation. By virtue of bilinear expression, its solitary waves are computed in a very direct method. By using the Riemann theta function, we derive the quasiperiodic solutions for the equation under some limitation factors. Besides, an effective way can be used to calculate its homoclinic breather waves and rogue waves, respectively, by using an extended homoclinic test function. We hope that our results can help enrich the dynamical behavior of the nonlinear wave equations with variable-coefficient.

Keywords:

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