General lump solutions, lumpoff solutions, and rogue wave solutions with predictability for the (2+1)-dimensional Korteweg-de Vries equation

Wang, Hui; Tian, Shou‐Fu; Zhang, Tiantian; Chen, Yi; Fang, Yong

doi:10.1007/s40314-019-0938-x

Cited by 14 publications

(5 citation statements)

References 61 publications

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“…There are many kinds of solutions that can be obtained by solving NLEEs in different ways, such as soliton solutions, breather wave solutions, lump solutions, periodic solutions, trigonometric solutions, and interaction of different solutions. [16][17][18][19] Among them, soliton solutions are one of the most important research topics. N-soliton solutions are exact multiple wave solutions of the integrable equations and are important for describing nonlinearities in areas such as shallow water waves, plasma, and nonlinear optics.…”

Section: Introductionmentioning

confidence: 99%

Interaction solutions and localized waves to the (2+1)-dimensional Hirota–Satsuma–Ito equation with variable coefficient

2023

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This article investigates the Hirota-Satsuma-Ito equation with variable coefficient using the Hirota bilinear method and the long wave limit method. The equation is proved to be Painlevé integrable by Painlevé analysis. On the basis of the bilinear form, the forms of two-soliton solutions, three-soliton solutions and four-soliton solutions are studied specifically. The appropriate parameter values are chosen and the corresponding figures are presented. The breather waves solutions, lump solutions, periodic solutions and the interaction of breather waves solutions and soliton solutions, etc are given in this article. In addition, we also analysed the different effects of the parameters on the figures. The figures of the same set of parameters in different planes are presented to describe the dynamical behaviour of solutions. These are important for describing water waves in nature.

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Section: Introductionmentioning

confidence: 99%

Interaction solutions and localized waves to the (2+1)-dimensional Hirota–Satsuma–Ito equation with variable coefficient

2023

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“…For the (2 þ 1)-dimensional KdV and mKdV equation that Wang and Kara derived in Wang and Kara (2019), they built both traveling wave and solitary wave solutions. Through the use of Bell's polynomial properties and the right transformation, Wang et al (2019b) were able to obtain a bilinear representation of the (2 þ 1)-dimensional KdV equation. Its lump solutions with localized properties were constructed in detail based on the discovered Hirota bilinear form.…”

Section: Introductionmentioning

confidence: 99%

New approach for soliton solutions for the (2 + 1)-dimensional KdV equation describing shallow water wave

Khuri

2022

HFF

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Purpose The purpose of this study is to produce families of exact soliton solutions (2+1)-dimensional Korteweg-de Vries (KdV) equation, that describes shallow water waves, using an ansätze approach. Design/methodology/approach This article aims to introduce a recently developed ansätze for creating soliton and travelling wave solutions to nonlinear nonintegrable partial differential equations, especially those with physical significance. Findings A recently developed ansätze solution was used to successfully construct soliton solutions to the (2 + 1)-dimensional KdV equation. This straightforward method is an alternative to the Painleve test analysis, yielding similar results. The strategy demonstrated the existence of a single soliton solution, also known as a localized wave or bright soliton, as well as singular solutions or kink solitons. Originality/value The ansätze solution used to construct soliton solutions to the (2 + 1)-dimensional KdV equation is novel. New soliton solutions were also obtained.

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“…The solitary wave solutions, which characterized nonlinear evolution equations (NLEEs), have many essential applications in physics and nonlinear disciplines, for instance, the Korteweg‐de Vries, Schrödinger, and B‐type Kadomtsev‐Petviashvili equations 30–33 …”

Section: Introductionmentioning

confidence: 99%

“…[27][28][29] The solitary wave solutions, which characterized nonlinear evolution equations (NLEEs), have many essential applications in physics and nonlinear disciplines, for instance, the Korteweg-de Vries, Schrödinger, and B-type Kadomtsev-Petviashvili equations. [30][31][32][33] In 2011, Vitanov et al 34 have presented a modified version of simplest equation method by using the Bernoulli equation ϕ y ¼ aϕ K þ bϕ and have constructedanalytical solutions of b-equation and generalized Degasperis-Processi equation and further applied in Vitanov 35 and Shao et al 36 Hassan et al 37 have used the modified method of simplest equation (34) to obtain explicit exact solutions of some NLEEs and further applied in Sun et al 38 In 2020, Kudryashov presented a new function 39 for constructing the solitary wave solutions of NPDEs belonging to the class of Schrödinger equations and has clarified that this new function is very effective in simplifying the complicated computations for extracting solitary wave solutions of higher order Schrödinger equations and further applications. 40,41 Our motivation in this paper is to use the simplest equation method and the Kudryashov new function method to extract new abundant solitary wave solutions for a variety of NPDEs modeling the propagation of waves on water surface, namely, the following equations: I.…”

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confidence: 99%

New abundant solitary wave structures for a variety of some nonlinear models of surface wave propagation with their geometric interpretations

El‐Ganaini

Al‐Amr

2022

Math Methods in App Sciences

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The propagation of waves of water on the surface is characterized by various mathematical models. In this work, we adopt the simplest equation method as well as the Kudryashov's new function method, to a variety of some nonlinear models of surface wave propagation to extract their abundant solitary wave structures. These nonlinear models include the Benjamin‐Bona‐Mahony (BBM) equation, the Ostrovsky (OS) equation, the Ostrovsky‐Benjamin‐Bona‐Mahony (OS‐BBM) equation, and the Boussinesq system of equations. Based on the solutions of two distinct auxiliary equations, various wave solutions are successfully obtained. In addition, the geometric interpretations of the obtained solutions are analyzed. To illuminate the physical nature of the obtained solutions of this paper, some graphical representations (numerical simulations) of the acquired solutions have been depicted in two‐dimensional density, two‐ and three‐dimensional graphs. Furthermore, a comparison between the obtained results of this paper and the solutions for the considered models obtained in the literature is also provided. It is shown that the used approaches are very effective and powerful strategies for a wider class of nonlinear partial differential equations in physical problems.

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General lump solutions, lumpoff solutions, and rogue wave solutions with predictability for the (2+1)-dimensional Korteweg-de Vries equation

Cited by 14 publications

References 61 publications

Interaction solutions and localized waves to the (2+1)-dimensional Hirota–Satsuma–Ito equation with variable coefficient

Interaction solutions and localized waves to the (2+1)-dimensional Hirota–Satsuma–Ito equation with variable coefficient

New approach for soliton solutions for the (2 + 1)-dimensional KdV equation describing shallow water wave

New abundant solitary wave structures for a variety of some nonlinear models of surface wave propagation with their geometric interpretations

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