Some lump solutions for a generalized (3+1)-dimensional Kadomtsev–Petviashvili equation

Guan, Xue; Liu, Wenjun; Zhou, Qin; Biswas, Anjan

doi:10.1016/j.amc.2019.124757

Cited by 55 publications

(23 citation statements)

References 26 publications

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“…is the soliton wave number and, θ is the phase constant. If we use the transformation given by (6) in the Equation (4) and separate the real and imaginary parts, a pair of relations emerges. The real part equation gives…”

Section: Mathematical Modelmentioning

confidence: 99%

A third-order nonlinear Schrödinger equation: the exact solutions, group-invariant solutions and conservation laws

Yaşar

Seadawy

2020

Journal of Taibah University for Science

119

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In this study, we consider the third order nonlinear Schrödinger equation (TONSE) that models the wave pulse transmission in a time period less than one-trillionth of a second. With the help of the extended modified method, we obtain numerous exact travelling wave solutions containing sets of generalized hyperbolic, trigonometric and rational solutions that are more general than classical ones. Secondly, we construct the transformation groups which left the equations invariant and vector fields with the Lie symmetry groups approach. With the help of these vector fields, we obtain the symmetry reductions and exact solutions of the equation. The obtained groupinvariant solutions are Jacobi elliptic function and exponential type. We discuss the dynamic behaviour and structure of the exact solutions for distinct solutions of arbitrary constants. Lastly, we obtain conservation laws of the considered equation by construing the complex equation as a system of two real partial differential equations (PDEs).

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Section: Mathematical Modelmentioning

confidence: 99%

A third-order nonlinear Schrödinger equation: the exact solutions, group-invariant solutions and conservation laws

Yaşar

Seadawy

2020

Journal of Taibah University for Science

119

View full text Add to dashboard Cite

show abstract

“…Moreover, their mathematical structures have also been presented to literature. Therefore, many effective methods such as (m + G /G)-expansion method [1,2], (1/G )-expansion method [3][4][5], rational sine-cosine function method [6], F-expansion method [7], Clarkson-Kruskal (CK) direct method [8], (G /G)-expansion method [9], Bäcklund transformation method [10], modified exp(−Ω(ξ))-expansion function [11], the Painlevé analysis [12], (G /G, 1/G)-expansion method [13], modified Laplace decomposition method [14], Hirota bilinear method [15,16], homotopy analysis method [17], modified Kudryashov method [18], etc. have been presented to the literature for observing of deeper properties of these models.…”

Section: Introductionmentioning

confidence: 99%

Novel Complex Wave Solutions of the (2+1)-Dimensional Hyperbolic Nonlinear Schrödinger Equation

2020

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“…Here, we will study the explicit solitary wave solutions of the model called generalized (3 + 1)‐D KP (gKP) equation, 39 which reads

{normalΨ}_{x x x y} + 3 {false({normalΨ}_{x} {normalΨ}_{y} false)}_{x} + α {normalΨ}_{x x x z} + 3 α {false({normalΨ}_{x} {normalΨ}_{z} false)}_{x} + λ_{1} {normalΨ}_{x t} + λ_{2} {normalΦ}_{y t} + λ_{3} {normalΦ}_{z t} + ω_{1} {normalΦ}_{x z} + ω_{2} {normalΦ}_{y z} + ω_{3} {normalΦ}_{z z} = 0,

where Ψ shows the velocity of the fluid in x ‐direction and where the function

normalΨ = normalΨ false(x, y, z, t false)

is the function of x , y , z , and t . The values of parameters α , λ j , and ω j , (

j = 1,2, 3

) are free values.…”

Section: Introductionmentioning

confidence: 99%

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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Some lump solutions for a generalized (3+1)-dimensional Kadomtsev–Petviashvili equation

Cited by 55 publications

References 26 publications

A third-order nonlinear Schrödinger equation: the exact solutions, group-invariant solutions and conservation laws

A third-order nonlinear Schrödinger equation: the exact solutions, group-invariant solutions and conservation laws

Novel Complex Wave Solutions of the (2+1)-Dimensional Hyperbolic Nonlinear Schrödinger Equation

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

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