Dynamics of heterotypic soliton, high-order breather, M-lump wave, and multi-wave interaction solutions for a ($$3+1$$)-dimensional Kadomtsev–Petviashvili equation

Zhong, Jie; Ma, Zhimin; Lei, Ruoyang; Liang, Jiang; Wang, Yongli

doi:10.1140/epjp/s13360-024-05082-6

Eur. Phys. J. Plus

2024

DOI: 10.1140/epjp/s13360-024-05082-6

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Dynamics of heterotypic soliton, high-order breather, M-lump wave, and multi-wave interaction solutions for a ($$3+1$$)-dimensional Kadomtsev–Petviashvili equation

Jie Zhong,

Zhimin Ma,

Ruoyang Lei

et al.

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2024

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Cited by 2 publications

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Multiple solitons, multiple lump solutions, and lump wave with solitons for a novel (2+1)-dimensional nonlinear partial differential equation

Ma,

Han,

Tian

2024

Phys. Scr.

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The primary aim of this paper is to explore exact solutions to a novel (2+1)-dimensional water wave equation that models oceanic wave phenomena. We begin by applying the Hirota bilinear transformation method to derive multi-soliton solutions, including 3-soliton and 4-soliton solutions. Then, utilizing the bilinear form of the equation and the long-wave limit method, we identify multiple lump solutions and interaction solutions between lumps and solitons. These include 1-lump, 2-lump, and 3-lump solutions, as well as interactions between a 1-lump and a 1-soliton, and between a 1-lump and 2-solitons. The physical dynamics of these solutions are visually represented, offering insight into the corresponding oceanic wave phenomena.

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Multiple solitons, multiple lump solutions, and lump wave with solitons for a novel (2+1)-dimensional nonlinear partial differential equation

Ma,

Han,

Tian

2024

Phys. Scr.

View full text Add to dashboard Cite

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Superposition of soliton, breather and lump waves in a non-painlevé integrabale extension of the Boiti-Leon-Manna-Pempinelli equation

Asadi,

Hosseini,

Madadi

2024

Phys. Scr.

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In this paper, we derive general $N$th-order Pfaffian solutions for a $(3+1)$-dimensional non-Painlev{'e} integrable extension of the Boiti-Leon-Manna-Pempinelli (BLMP) equation. Specifcally, we obtain $N$-soliton, higher-order breather, higher-order lump and hybrid solutions, and explore the superpositions of Y-shaped and X-shaped soliton-breather waves.Moreover, we construct bilinear B"{a}cklund transformations, Lax pairs, and conservation laws using Bell polynomials.Finally, we identify a similar equation in the literature and demonstrate that it represents another non-Painlevé integrable extension of the BLMP equation.

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Dynamics of heterotypic soliton, high-order breather, M-lump wave, and multi-wave interaction solutions for a ($$3+1$$)-dimensional Kadomtsev–Petviashvili equation

Cited by 2 publications

References 40 publications

Multiple solitons, multiple lump solutions, and lump wave with solitons for a novel (2+1)-dimensional nonlinear partial differential equation

Multiple solitons, multiple lump solutions, and lump wave with solitons for a novel (2+1)-dimensional nonlinear partial differential equation

Superposition of soliton, breather and lump waves in a non-painlevé integrabale extension of the Boiti-Leon-Manna-Pempinelli equation

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