A variety of (3 + 1)‐dimensional Burgers equations derived by using the Burgers recursion operator

Wazwaz, Abdul‐Majid

doi:10.1002/mma.3255

Cited by 6 publications

(4 citation statements)

References 25 publications

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“…The fully non-elastic interaction phenomenon between the kink soliton and rogue wave appears in the (2 þ 1)-dimensional Burgers' equation (Tan and Dai, 2016). Moreover, similar phenomena have been observed in many nonlinear science fields such as passive random walk dynamics, gas dynamics, hydrodynamics, plasma physics, laser and optical physics, electromagnetics and nuclear physics (Wazwaz, 2013;Kibler et al, 2010;Ganshin et al, 2008;Kibler et al, 2012).…”

Section: Introductionmentioning

confidence: 64%

Lump solutions and interaction phenomena of the (3 + 1)-dimensional nonlinear evolution equations

Mao

Tian

Yan

et al. 2019

HFF

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Purpose The purpose of this study is to examine the lump solutions of the (3 + 1)-dimensional nonlinear evolution equations by considering a (3 + 1)-dimensional generalized Kadomtsev–Petviashvili (gKP) equation and a (3 + 1)-dimensional variable-coefficient generalized B-type Kadomtsev–Petviashvili (vcgBKP) equation as examples. Design/methodology/approach Based on Hirota’s bilinear theory, a direct method is used to examine the lump solutions of these two equations. Findings The complete non-elastic interaction solutions between a lump and a stripe are also discussed for the equations, which show that the lump solitons are swallowed by the stripe solitons. Originality/value The dynamics of these solutions are analyzed to enrich the diversity of the dynamics of high-dimensional KP-type nonlinear wave equations.

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Section: Introductionmentioning

confidence: 64%

Lump solutions and interaction phenomena of the (3 + 1)-dimensional nonlinear evolution equations

Mao

Tian

Yan

et al. 2019

HFF

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“…(26) with the aid of Mathematica as Wazwaz [26,29] obtained multiple kink solutions of Eq. (12) by using simplied Hirota's method and found multiple soliton solutions by using the HeremanNuseir method.…”

Section: Fig 1 the Prole Of Solution Eq (18)mentioning

confidence: 99%

New Applications of the (G'/G,1/G)-Expansion Method

İnan

Uğurlu

2015

Acta Phys. Pol. A

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“…[21][22][23] Burgers' equation can be reduced to a linear equation under the Cole-Hopf transformation, then the analytical solutions can be derived, and some Burgers-type NLEEs which cannot be linearized directly have been solved via the Hirota method. [33][34][35] Coupled NLEEs have been considered, such as the generalized variable-coefficient Drinfeld-Sokolov-Satsuma-Hirota system, [36] Downloaded by [University of Nebraska, Lincoln] at 17:03 31 May 2016 coupled KdV-mKdV system, [37] and (2+1)-dimensional Boiti-Leon-Pempinelli system for water waves. [38] To our knowledge, analytic properties such as the soliton solutions and bilinear BT for Equation (3) have not been studied via the binary Bell polynomials.…”

Section: Introductionmentioning

confidence: 99%

Multi-soliton solutions and Bäcklund transformation for a two-mode KdV equation in a fluid

Xiao

Tian

Zhen

et al. 2016

Waves in Random and Complex Media

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2016): Multisoliton solutions and Bäcklund transformation for a two-mode KdV equation in a fluid, Waves in Random and Complex Media, ABSTRACTIn this paper, we investigate a two-mode Korteweg-de Vries equation, which describes the one-dimensional propagation of shallow water waves with two modes in a weakly nonlinear and dispersive fluid system. With the binary Bell polynomial and an auxiliary variable, bilinear forms, multi-soliton solutions in the two-wave modes and Bell polynomial-type Bäcklund transformation for such an equation are obtained through the symbolic computation. Soliton propagation and collisions between the two solitons are presented. Based on the graphic analysis, it is shown that the increase in s can lead to the increase in the soliton velocities under the condition of α = β = 1, but the soliton amplitudes remain unchanged when s changes, where s means the difference between the phase velocities of twomode waves, α and β are the nonlinearity parameter and dispersion parameter respectively. Elastic collisions between the two solitons in both two modes are analyzed with the help of graphic analysis. ARTICLE HISTORY

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A variety of (3 + 1)‐dimensional Burgers equations derived by using the Burgers recursion operator

Cited by 6 publications

References 25 publications

Lump solutions and interaction phenomena of the (3 + 1)-dimensional nonlinear evolution equations

Lump solutions and interaction phenomena of the (3 + 1)-dimensional nonlinear evolution equations

New Applications of the (G'/G,1/G)-Expansion Method

Multi-soliton solutions and Bäcklund transformation for a two-mode KdV equation in a fluid

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