Lie group analysis, analytic solutions and conservation laws of the (3 + 1)-dimensional Zakharov-Kuznetsov-Burgers equation in a collisionless magnetized electron-positron-ion plasma

Du, Xia‐Xia; Tian, Bo; Wu, Xiao-Yu; Yin, Hui-Min; Zhang, Chen-Rong

doi:10.1140/epjp/i2018-12239-y

Cited by 64 publications

(13 citation statements)

References 45 publications

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“…Hu et al in [5] explored the mixed lump-kink and rogue wavekink solutions for a (3 + 1)-dimensional B-type Kadomtsev-Petviashvili equation in fluid mechanics. Further, many interesting soliton-type solutions for physical applications that arise in plasma, surface waves of finite depth, and optical fiber were studied by researchers in, e.g., [6][7][8][9].…”

Section: Introductionmentioning

confidence: 99%

Stationary wave solutions for new developed two-waves’ fifth-order Korteweg–de Vries equation

et al. 2019

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In this work, we present a new two-waves' version of the fifth-order Korteweg-de Vries model. This model describes the propagation of moving two-waves under the influence of dispersion, nonlinearity, and phase velocity factors. We seek possible stationary wave solutions to this new model by means of Kudryashov-expansion method and sine-cosine function method. Also, we provide a graphical analysis to show the effect of phase velocity on the motion of the obtained solutions. MSC: 35C08; 74J35

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Section: Introductionmentioning

confidence: 99%

Stationary wave solutions for new developed two-waves’ fifth-order Korteweg–de Vries equation

et al. 2019

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“…The first‐ and second‐order rogue wave solutions and interactions between the first‐order rogue waves with solitons and soliton, degenerate‐soliton, periodic, and soliton‐like rational solutions with binary Darboux transformation were constructed for nonlinear Schrödinger equation. In a previous study, Du et al derived the Lie point symmetry generators and Lie symmetry groups for the (3+1)‐dimensional Zakharov‐Kuznetsov‐Burgers equation . By using symbolic computation, Hu et al obtained the mixed lump‐kink and mixed rogue wave‐kink solutions for the B‐type KP equation.…”

Section: Introductionmentioning

confidence: 99%

Breather wave, periodic, and cross‐kink solutions to the generalized Bogoyavlensky‐Konopelchenko equation

Manafian

Ivatloo

Abapour

2019

Math Methods in App Sciences

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The present article deals with multi-waves and breather wave solutions of the generalized Bogoyavlensky-Konopelchenko equation by virtue of the Hirota bilinear operator method and the semi-inverse variational principle. The obtained solutions for solving the current equation represent some localized waves including soliton, periodic, and cross-kink solutions in which have been investigated by the approach of the bilinear method. With certain parameter constraints in the multi-waves and breather, all cases of the periodic and cross-kink solutions can be captured from the one and two soliton(s). The obtained solutions are extended with numerical simulation to analyze graphically, which results into 1-and 2-soliton solutions and also periodic and cross-kink solutions profiles, that will be extensively used to report many attractive physical phenomena in the fields of acoustics, heat transfer, fluid dynamics, classical mechanics, and so on. KEYWORDS generalized Bogoyavlensky-Konopelchenko equation, Hirota bilinear operator method, multi-waves and breather, periodic and cross-kink solutions, semi-inverse variational principle, solitons MSC CLASSIFICATION

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“…The features of NLSE are contributed in text books on nonlinear optics . There are several other equations such as NLSE, sine‐Gordon equation, Zakharov‐Kuznetsov‐Burgers equation, Kadomtsev‐Petviashvili‐Burgers type equation, B‐type Kadomtsev‐Petviashvili equation, Kadomtsev‐Petviashvili equation, and many more are reviewed in References . The researchers have explored extended form of NLSE to explain the transmission of optical pulse in nonlinear and nonlocal feeble media.…”

Section: Introductionmentioning

confidence: 99%

Generation and transmission of fractional‐order optical bright solitons in single mode fiber

Mehboob

Usman

Hussain

2019

Micro & Optical Tech Letters

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This article addresses the generation and transmission of fractional-order optical bright solitons (OBSs) in silica based single mode fiber. We take into account secondorder dispersion effect in the presence of anomalous dispersion and self-phase modulation together with third-order dispersion. Fractional-order OBS have been extracted using nonlinear Schrodinger equation. We consider dispersion dominant case with variation of data rates from 10 to 60 Gbps covering ultralong distance of 9040 km. The transmission link is composed of optical amplifier with gain of 20 dB and a noise figure of 4 dB. The analytical computations are carried out to calculate the nonlinear dispersive effects and a comparison is made between the analytical and simulated results. Erbiumdoped fiber amplifier and dispersion compensated fiber have been used to overcome fluctuations and to maintain the fractional-order OBS pulse profile. In the end, the outcomes are probed and compared on the basis of Q-factor and bit error rate (BER). It is observed that best OBS transmission result is achieved at 40 Gbps, where Q-factor is 9.85 with a corresponding BER of 2.91e −23 . K E Y W O R D S nonlinear Schrodinger equation, optical bright solitons, second-order dispersion, self-phase modulation, third-order dispersion

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Lie group analysis, analytic solutions and conservation laws of the (3 + 1)-dimensional Zakharov-Kuznetsov-Burgers equation in a collisionless magnetized electron-positron-ion plasma

Cited by 64 publications

References 45 publications

Stationary wave solutions for new developed two-waves’ fifth-order Korteweg–de Vries equation

Stationary wave solutions for new developed two-waves’ fifth-order Korteweg–de Vries equation

Breather wave, periodic, and cross‐kink solutions to the generalized Bogoyavlensky‐Konopelchenko equation

Generation and transmission of fractional‐order optical bright solitons in single mode fiber

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