Resonant multiple wave, periodic wave and interaction solutions of the new extended (3 + 1)-dimensional Boiti-Leon-Manna-Pempinelli equation

Wang, Kang‐Jia

doi:10.1007/s11071-023-08699-x

Cited by 46 publications

(5 citation statements)

References 56 publications

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“…where ℓ i , β i , γ i , and ω i are the non-zero constants that we can identify later. On the basis of the linear superposition principle (LSP) [51,52], we have:…”

Section: The Non-singular Complexiton Solutionsmentioning

confidence: 99%

Non‐singular complexiton, singular complexiton and complex multiple soliton solutions to the (3 + 1)‐dimensional nonlinear evolution equation

Wang,

Shi,

et al. 2024

Math Methods in App Sciences

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This research mainly concerned with some new solutions of the (3 + 1)‐dimensional nonlinear evolution equation (NEE). First, we extract the resonant multiple soliton solutions (RMSSs) by taking advantage of the linear superposition principle (LSP) and weight algorithm (WA). Then the non‐singular complexiton and singular complexiton solutions are developed by introducing pairs of the conjugate parameters. Besides, the complex multiple‐soliton solutions are also explored with the aid of the bilinear approach. The graph descriptions of the attained solutions are paraded to show the dynamical properties. The outcomes of this work are all new and are desirous to bring some new perspective to the investigation of the complexiton solutions to the other partial differential equations (PDEs).

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“…where ℓ i , β i , γ i , and ω i are the non-zero constants that we can identify later. On the basis of the linear superposition principle (LSP) [51,52], we have:…”

Section: The Non-singular Complexiton Solutionsmentioning

confidence: 99%

Non‐singular complexiton, singular complexiton and complex multiple soliton solutions to the (3 + 1)‐dimensional nonlinear evolution equation

Wang,

Shi,

et al. 2024

Math Methods in App Sciences

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“…For obtaining the bilinear form of equation (1.1), we introduce the Cole–Hopf transform as (Wang, 2023): …”

Section: The Bilinear Form and The Exact Solutionsmentioning

confidence: 99%

Dynamics of breather, multi-wave, interaction and other wave solutions to the new (3+1)-dimensional integrable fourth-order equation for shallow water waves

Wang

2023

HFF

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Purpose The purpose of this paper is to study the new (3 + 1)-dimensional integrable fourth-order nonlinear equation which is used to model the shallow water waves. Design/methodology/approach By means of the Cole–Hopf transform, the bilinear form of the studied equation is extracted. Then the ansatz function method combined with the symbolic computation is implemented to construct the breather, multiwave and the interaction wave solutions. In addition, the subequation method tis also used to search for the diverse travelling wave solutions. Findings The breather, multiwave and the interaction wave solutions and other wave solutions like the singular periodic wave structure and dark wave structure are obtained. To the author’s knowledge, the solutions obtained are all new and have never been reported before. Originality/value The solutions obtained in this work have never appeared in other literature and can be regarded as an extension of the solutions for the new (3 + 1)-dimensional integrable fourth-order nonlinear equation.

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“…In [47], the interaction solutions between the N-soliton and lump solutions are studied. In [48], the resonant multiple soliton solutions are investigated. In [49], the soliton of the lump type and breather type are found.…”

Section: Introductionmentioning

confidence: 99%

Non-singular complexiton, singular complexiton and complex N-soliton solutions of the new extended (3+1)-dimensional Boiti-Leon-Manna-Pempinelli equation

Wang,

Shi

2024

Phys. Scr.

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The central target of this work is to extract some novel exact solutions of the new extended (3+1)-dimensional Boiti-Leon-Manna-Pempinelli equation (BLMPE) for the incompressible fluid. By applying the weight algorithm (WA) and linear superposition principle (LSP), we construct two sets of the complexiton solutions, which are the non-singular complexiton and singular complexiton solution via introducing the pairs of the conjugate parameters. In addition, we also explore the complex N-soliton solutions (CNSSs) via the Hirota bilinear equation (HBE) that is developed by the Cole-Hopf transform (CHT). The outlines of the corresponding exact solutions are presented graphically. As far as the information currently available, the derived solutions in this exploration are all new and are expected to enable us to investigate the dynamic characteristics of the considered equation better.

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Resonant multiple wave, periodic wave and interaction solutions of the new extended (3 + 1)-dimensional Boiti-Leon-Manna-Pempinelli equation

Cited by 46 publications

References 56 publications

Non‐singular complexiton, singular complexiton and complex multiple soliton solutions to the (3 + 1)‐dimensional nonlinear evolution equation

Non‐singular complexiton, singular complexiton and complex multiple soliton solutions to the (3 + 1)‐dimensional nonlinear evolution equation

Dynamics of breather, multi-wave, interaction and other wave solutions to the new (3+1)-dimensional integrable fourth-order equation for shallow water waves

Non-singular complexiton, singular complexiton and complex N-soliton solutions of the new extended (3+1)-dimensional Boiti-Leon-Manna-Pempinelli equation

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