A symbolic computation approach to constructing rogue waves with a controllable center in the nonlinear systems

Zhaqilao, Zhaqilao

doi:10.1016/j.camwa.2018.02.001

Cited by 71 publications

(31 citation statements)

References 34 publications

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“…Here, we give a brief description of multiple rouge wave solution technique. This section clarifies a systematic proclamation of multiple rogue wave solution [45][46][47] so that it can be more employed to the nonlinear PDEs until its exact solutions are determined. Phase 1.…”

Section: Multiple Rouge Wave Solution Methodsmentioning

confidence: 99%

“…According to the stated technique in Section 2 introduced by Zhaqilao, 45 we extract the higher order rogue wave solutions in the controllable center of the generalized (2 + 1)-dimensional KP equation. Taking into account n = 0 at (2.5), afterwards, (2.5) can be written as…”

Section: Category I: One-wave Solutionmentioning

confidence: 99%

“…43 The analytical treatment of N-soliton, lump, and lump-kink solutions of time-fractional KP equation has been studied in Hamid et al 44 Hereafter, we will investigate the multiple rogue waves for finding the multifold soliton solutions. The multiple rogue waves technique was employed by a lot of powerful researchers for diverse nonlinear equations to building rogue waves solutions with a controllable center (see other studies for detail [45][46][47][48] ). Therefore, the foremost concern for the researchers is to find the exact solutions of NLPDEs.…”

Section: Introductionmentioning

confidence: 99%

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Multiple rogue wave, lump‐periodic, lump‐soliton, and interaction betweenk‐lump andk‐stripe soliton solutions for the generalized KP equation

Zhao

Manafian

Zaya

et al. 2020

Math Methods in App Sciences

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The multiple rogue wave solutions technique is engaged to seek the multifold soliton solutions for the generalized (2 + 1)‐dimensional Kadomtsev–Petviashvili (gKP) equation, which contains one wave, two waves, and triple waves solutions. The second‐order derivative will be perused to get the minimum or maximum amount of lump solution. For one case, the lump solution will be shown the bright‐dark lump structure, and for another case, the dark lump structure two small peaks and one deep hole can be present. Also, the interaction of lump with periodic waves and the interaction between the lump and two stripe solitons can be catched by introducing the Hirota forms. Simultaneously, the interaction between k‐lump and k‐stripe soliton wave solutions can be gained by the Hirota operator. The physical phenomena of these gained multiple soliton solutions are analyzed and indicated in diagrams by choosing proper amounts.

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Section: Multiple Rouge Wave Solution Methodsmentioning

confidence: 99%

Section: Category I: One-wave Solutionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Multiple rogue wave, lump‐periodic, lump‐soliton, and interaction betweenk‐lump andk‐stripe soliton solutions for the generalized KP equation

Zhao

Manafian

Zaya

et al. 2020

Math Methods in App Sciences

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“…The high-order lumps of the (3+1)-dimensional KP-Boussinesq equation were presented by using Hirota's bilinear method [39]. Zhaqilao et al proposed a new method to construct the multiple lump solutions with a controllable center [40,41]. We constructed the multiple lump solutions of the (3+1)-dimensional potential Yu-Toda-Sasa-Fukuyama equation [42].…”

Section: Complexitymentioning

confidence: 99%

Rogue Wave and Multiple Lump Solutions of the (2+1)‐Dimensional Benjamin‐Ono Equation in Fluid Mechanics

Zhao

Gao

2019

Complexity

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In this paper, the bilinear method is employed to investigate the rogue wave solutions and the rogue type multiple lump wave solutions of the (2+1)-dimensional Benjamin-Ono equation. Two theorems for constructing rogue wave solutions are proposed with the aid of a variable transformation. Four kinds of rogue wave solutions are obtained by means of Theorem 1. In Theorem 2, three polynomial functions are used to derive multiple lump wave solutions. The 3-lump solutions, 6-lump solutions, and 8lump solutions are presented, respectively. The 3-lump wave has a "triangular" structure. The centers of the 6-lump wave form a pentagram around a single lump wave. The 8-lump wave consists of a set of seven first order rogue waves and one second order rogue wave as the center. The multiple lump wave develops into low order rogue wave as parameters decline to zero. The method presented in this paper provides a uniform method for investigating high order rational solutions. All the results are useful in explaining high dimensional dynamical phenomena of the (2+1)-dimensional Benjamin-Ono equation.

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“…However, we limit our objective to pursue only its integrability nature through Painlevé analysis and the dynamics of associate rogue waves in this work. Particularly, we are interested to construct higher order rogue wave solutions of the considered HSI model based on Hirota bilinear formalism and generalized polynomial test functions [43,44,45,46,47] and to explore their dynamics through a detailed discussion on the effect of system parameters. It is shown that the considered methodology to construct higher-order rogue waves was proven to be effective with higher-dimensional nonlinear models too [43,44,45,46,47].…”

Section: Introductionmentioning

confidence: 99%

Painlevé Analysis and Higher-Order Rogue Waves of a Generalized(3+1)-dimensional Shallow Water Wave Equation

Singh,

Sakkaravarthi,

Tamizhmani

et al. 2021

Preprint

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Considering the importance of ever-increasing interest in exploring localized waves, we investigate a generalized (3+1)-dimensional Hirota-Satsuma-Ito equation describing the unidirectional propagation of shallow-water waves and perform Painlevé analysis to understand its integrability nature. We construct the explicit form of higher-order rogue wave solutions by adopting Hirota's bilinearization and generalized polynomial functions. Further, we explore their dynamics in detail, depicting different pattern formation that reveal potential advantages with available arbitrary constants in their manipulation mechanism. Particularly, we demonstrate the existence of singly-localized line-rogue waves and doubly-localized rogue waves with multiple (single, triple, and sextuple) structures generating triangular and pentagon type geometrical patterns with controllable orientations that can be altered appropriately by tuning the parameters. The presented analysis will be an essential inclusion in the context of rogue waves in higher-dimensional systems.

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A symbolic computation approach to constructing rogue waves with a controllable center in the nonlinear systems

Cited by 71 publications

References 34 publications

Multiple rogue wave, lump‐periodic, lump‐soliton, and interaction betweenk‐lump andk‐stripe soliton solutions for the generalized KP equation

Multiple rogue wave, lump‐periodic, lump‐soliton, and interaction betweenk‐lump andk‐stripe soliton solutions for the generalized KP equation

Rogue Wave and Multiple Lump Solutions of the (2+1)‐Dimensional Benjamin‐Ono Equation in Fluid Mechanics

Painlevé Analysis and Higher-Order Rogue Waves of a Generalized(3+1)-dimensional Shallow Water Wave Equation

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