Rational and semi-rational solutions of the Kadomtsev–Petviashvili-based system

Zhang, Yongshuai; Rao, J. V.; Porsezian, K.; He, Jingsong

doi:10.1007/s11071-018-4620-4

Cited by 10 publications

(6 citation statements)

References 55 publications

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“…[10][11][12][13][14] RWs in high-dimensional systems are often called line RWs, which are merely localized in time. [15][16][17][18] The study of RW has been widely used in diverse areas of theoretical and applied physics, including plasma physics, [19,20] Bose-Einstein condensates, [21,22] atmosphere physics, [23] optics and photonics, [24][25][26] and superfluids. [27] Now, a fundamental problem can be asked: Is it possible that other types of RW solutions exist in nonlinear systems?…”

Section: Introductionmentioning

confidence: 99%

Deformed two-dimensional rogue waves in the (2+1)-dimensional Korteweg-de Vries equation*

Cao

Cheng

et al. 2021

Chinese Phys. B

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Within the (2 + 1)-dimensional Korteweg–de Vries equation framework, new bilinear Bäcklund transformation and Lax pair are presented based on the binary Bell polynomials and gauge transformation. By introducing an arbitrary function ϕ(y), a family of deformed soliton and deformed breather solutions are presented with the improved Hirota’s bilinear method. By choosing the appropriate parameters, their interesting dynamic behaviors are shown in three-dimensional plots. Furthermore, novel rational solutions are generated by taking the limit of the obtained solitons. Additionally, two-dimensional (2D) rogue waves (localized in both space and time) on the soliton plane are presented, we refer to them as deformed 2D rogue waves. The obtained deformed 2D rogue waves can be viewed as a 2D analog of the Peregrine soliton on soliton plane, and its evolution process is analyzed in detail. The deformed 2D rogue wave solutions are constructed successfully, which are closely related to the arbitrary function ϕ(y). This new idea is also applicable to other nonlinear systems.

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Section: Introductionmentioning

confidence: 99%

Deformed two-dimensional rogue waves in the (2+1)-dimensional Korteweg-de Vries equation*

Cao

Cheng

et al. 2021

Chinese Phys. B

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“…[32], with soliton solutions in Wronskian form using bilinear formalism, and another case (viii) N-solitary wave, homoclinic breather, and rogue wave solutions of (3+1)D nonlinear wave equation when 5, 6, 7 [33]. Apart from the above listed models, different class of higherdimensional nonlinear equations under various physical settings have been reported with interesting results on rogue waves and interacting waves in the recent years, see for example [34][35][36][37][38][39][40][41][42][43]. Moreover, under the vanishing effect of the parameter Γ 2 = 0, the model (1) comes under the family of Hirota-Satsuma equations.…”

Section: Introductionmentioning

confidence: 99%

Painlevé analysis and higher-order rogue waves of a generalized (3+1)-dimensional shallow water wave equation

et al. 2022

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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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“…Further, various nonlinear wave solutions including periodic waves, lump solutions, multi-waves, and interaction waves, etc., of the above mentioned works have been reported. Apart from the above listed models, several types of higher-dimensional nonlinear equations under different physical situations have been reported with interesting results on rogue waves in the recent years, see for example [33,34,35,36,37,38,39,40,41,42]. From these different possible and existing models, it is clear that the considered (3+1)D Hirota-Satsuma-Ito equation (1.1) is more general with much physical importance.…”

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.

show abstract

Rational and semi-rational solutions of the Kadomtsev–Petviashvili-based system

Cited by 10 publications

References 55 publications

Deformed two-dimensional rogue waves in the (2+1)-dimensional Korteweg-de Vries equation*

Deformed two-dimensional rogue waves in the (2+1)-dimensional Korteweg-de Vries equation*

Painlevé analysis and higher-order rogue waves of a generalized (3+1)-dimensional shallow water wave equation

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

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