Dark breather waves, dark lump waves and lump wave–soliton interactions for a <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll" id="d1e1368" altimg="si37.gif"><mml:mrow><mml:mo>(</mml:mo><mml:mn>3</mml:mn><mml:mo>+</mml:mo><mml:mn>1</mml:mn><mml:mo>)</mml:mo></mml:mrow></mml:math>-dimensional generalized Kadomtsev–Petviashvili equation in a fluid

Hu, Cong-Cong; Yin, Hui-Min; Zhang, Chen-Rong; Zhang, Ze

doi:10.1016/j.camwa.2019.02.026

Cited by 64 publications

(12 citation statements)

References 42 publications

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“…at any arbitrary fixed time t. Also (8) is a critical points for u, v and w. It is noted that at these critical points (8), the function f (x, y, z, t) − a 6 vanishes. This means that f (x, y, z, t) > 0 if and only if a 6 > 0, which implies that u, v and w in (2) are analytical functions if and only if a 6 > 0.…”

Section: Lump Solitons For (3 + 1)-dimensional Burgers-like Equationmentioning

confidence: 98%

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Studying Lump solutions, Rogue wave solutions and dynamical interaction for new model generating from lax pair

Elboree

2020

Math. Model. Nat. Phenom.

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In this paper, we consider the (3 + 1)-dimensional Burgers-like equation which arises in fluid mechanics, which constructed from Lax pair generating technique. The bilinear form for this model is obtained to construct the multiple-kink solutions. Lump solution, rogue wave solutions are constructed via the obtained bilinear form for this model. The physical phenomena for these solution are analyzed by studying the influence of the parameters for these solutions. The phase shifts, propagation directions and amplitudes for these solutions are controlled via these parameters. .The collisions between the lump wave and the stripe soliton, which is called lumpo solution are completely nonelastic interaction. Finally, the figures of the solutions are shown to study the dynamical behavior for the lump, rogue wave and the properties of the interaction phenomena under various parameters for (3 + 1)-dimensional Burgers-like equation. These results can't be found in the previous scientific papers.

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Section: Lump Solitons For (3 + 1)-dimensional Burgers-like Equationmentioning

confidence: 98%

“…Lump solutions are localized and decay algebraically [6,7,8] and a special kind of rational solutions. Hirota bilinear method [9] is one of the approaches to study the lump solutions.…”

Section: Introductionmentioning

confidence: 99%

Studying Lump solutions, Rogue wave solutions and dynamical interaction for new model generating from lax pair

Elboree

2020

Math. Model. Nat. Phenom.

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“…Investigations on the shallow water waves have been carried out in environmental engineering and hydraulic engineering (Ablowitz, 2011; Vreugdenhil, 1994; Zdyrski and Feddersen, 2021; Karunakar and Chakraverty, 2021; Salehipour et al , 2013; Wazwaz, 2019; Redor et al , 2019; Benkhaldoun et al , 2013; Shen and Tian, 2021; Chen et al , 2021; Chakravarty and Kodama, 2014). Certain nonlinear evolution equations (NLEEs) have been proposed to model the shallow water waves, such as the Korteweg–de Vries equation, Kadomtsev–Petviashvili-type equations, dispersive long-wave systems, Whitham–Broer–Kaup systems and Broer–Kaup–Kupershmidt (BKK) systems (Israwi and Kalisch, 2019; Das and Mandal, 2021; Crabb and Akhmediev, 2021; Hu et al , 2019; Shen et al , 2021; Ablowitz and Baldwin, 2012; Gao et al , 2021a; Ma et al , 2021a; Sulaiman et al , 2021; Liu et al , 2021; Wang et al , 2020; Ebadi et al , 2015; Zhao et al , 2021; Cheng et al , 2021; Al-Shawba et al , 2020; Wazwaz, 2013; Kumar et al , 2016; Wazwaz, 2021; Ying and Lou, 2001).…”

Section: Introductionmentioning

confidence: 99%

Gramian solutions and solitonic interactions of a (2+1)-dimensional Broer–Kaup–Kupershmidt system for the shallow water

Gao

et al. 2021

HFF

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Purpose This paper aims to study the Gramian solutions and solitonic interactions of a (2 + 1)-dimensional Broer–Kaup–Kupershmidt (BKK) system, which models the nonlinear and dispersive long gravity waves traveling along two horizontal directions in the shallow water of uniform depth. Design/methodology/approach Pfaffian technique is used to construct the Gramian solutions of the (2 + 1)-dimensional BKK system. Asymptotic analysis is applied on the two-soliton solutions to study the interaction properties. Findings N-soliton solutions in the Gramian with a real function ζ(y) of the (2 + 1)-dimensional BKK system are constructed and proved, where N is a positive integer and y is the scaled space variable. Conditions of elastic and inelastic interactions between the two solitons are revealed asymptotically. For the three and four solitons, elastic, inelastic interactions and soliton resonances are discussed graphically. Effect of the wave numbers, initial phases and ζ(y) on the solitonic interactions is also studied. Originality/value Shallow water waves are studied for the applications in environmental engineering and hydraulic engineering. This paper studies the shallow water waves through the Gramian solutions of a (2 + 1)-dimensional BKK system and provides some phenomena that have not been studied.

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“…Multi-component and higher-order extensions of lump solutions exhibit diverse soliton phenomena, particularly the (3+1)-dimensional case always leads to multiple wave solutions and lump solutions. The aim of this study is to use the Hirota bilinear forms to generate the generalized (3+1) dimensional variable coefficient B-type Kadomtsev-Petviashvili equation [15][16][17]…”

Section: Introductionmentioning

confidence: 99%

Lump solutions for the dimensionally reduced variable coefficient B-type Kadomtsev-Petviashvili equation

Zhang

Zhao²,

Pang

2021

THERM SCI

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Dark breather waves, dark lump waves and lump wave–soliton interactions for a (3+1)-dimensional generalized Kadomtsev–Petviashvili equation in a fluid

Cited by 64 publications

References 42 publications

Studying Lump solutions, Rogue wave solutions and dynamical interaction for new model generating from lax pair

Studying Lump solutions, Rogue wave solutions and dynamical interaction for new model generating from lax pair

Gramian solutions and solitonic interactions of a (2+1)-dimensional Broer–Kaup–Kupershmidt system for the shallow water

Lump solutions for the dimensionally reduced variable coefficient B-type Kadomtsev-Petviashvili equation

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