(<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll" id="d1e317" altimg="si1.gif"><mml:mn>2</mml:mn><mml:mo>+</mml:mo><mml:mn>1</mml:mn></mml:math>)-dimensional ZK–Burgers equation with the generalized beta effect and its exact solitary solution

Yin, Xiaojun; Yang, Liangui; Liu, Quansheng; Wu, Guorong

doi:10.1016/j.camwa.2018.09.033

Cited by 8 publications

(2 citation statements)

References 34 publications

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“…Over the past decades, the non-linear PDE which arise in various fields of non-linear science are vastly studied to reveal the physical systems of all kinds of situations [1][2][3][4][5][6][7][8][9][10][11]. In the study of mathematical models, we pay more attention to find the exact solution and solitary solution of these equations.…”

Section: Introductionmentioning

confidence: 99%

The new exact solitary solutions for the (3+1)-dimensional Zakharov-Kuznetsov equation using the Riccati equation

et al. 2020

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In this paper, a non-linear (3+1)-dimensional Zakharov-Kuznetsov equation is investigated by employing the subsidiary equation method, which arises in quantum magneto plasma. The periodic solutions, rational wave solutions, soliton solutions for the quantum Zakharov-Kuznetsov equation which play an important role in mathematical physics are obtained with the help of the Riccati equation expan?sion method. Meanwhile, the electrostatic potential can be accordingly obtained. Compared to the other methods, the exact solutions obtained will extend on earlier reports by using the Riccati equation.

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Section: Introductionmentioning

confidence: 99%

The new exact solitary solutions for the (3+1)-dimensional Zakharov-Kuznetsov equation using the Riccati equation

et al. 2020

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“…The problem of wave-wave interaction is a very important one in the earth fluid, and further study can deepen people's understanding of large-scale motion phenomena in the atmosphere, ocean and large lakes. There are many motion equations describing Rossby waves in a layer of fluid, such as one-dimensional KdV equation [13], MKdV equation [14], Boussinesq equation [15] and high-dimensional ZK equation [16], mZK equation [17], KP equation [18] and so on. The actual atmospheric ocean system is very complex, compared with the single equation of low dimension, the coupled equations set [19][20][21]of high dimension are more practical.…”

Section: Introductionmentioning

confidence: 99%

Time-Space Fractional Coupled Generalized Zakharov-Kuznetsov Equations Set for Rossby Solitary Waves in Two-Layer Fluids

Chen

Yang

2019

Mathematics

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In this paper, the theoretical model of Rossby waves in two-layer fluids is studied. A single quasi-geostrophic vortex equation is used to derive various models of Rossby waves in a one-layer fluid in previous research. In order to explore the propagation and interaction of Rossby waves in two-layer fluids, from the classical quasi-geodesic vortex equations, by employing the multi-scale analysis and turbulence method, we derived a new (2+1)-dimensional coupled equations set, namely the generalized Zakharov-Kuznetsov(gZK) equations set. The gZK equations set is an extension of a single ZK equation; they can describe two kinds of weakly nonlinear waves interaction by multiple coupling terms. Then, for the first time, based on the semi-inverse method and the variational method, a new fractional-order model which is the time-space fractional coupled gZK equations set is derived successfully, which is greatly different from the single fractional equation. Finally, group solutions of the time-space fractional coupled gZK equations set are obtained with the help of the improved ( G ′ / G ) -expansion method.

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A Novel Generalized Method for Evolution Equation and its Application in Plasma

Raut¹,

Roy

Roy³

2022

Nonlinear Dynamics and Applications

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(2+1)-dimensional ZK–Burgers equation with the generalized beta effect and its exact solitary solution

Cited by 8 publications

References 34 publications

The new exact solitary solutions for the (3+1)-dimensional Zakharov-Kuznetsov equation using the Riccati equation

The new exact solitary solutions for the (3+1)-dimensional Zakharov-Kuznetsov equation using the Riccati equation

Time-Space Fractional Coupled Generalized Zakharov-Kuznetsov Equations Set for Rossby Solitary Waves in Two-Layer Fluids

A Novel Generalized Method for Evolution Equation and its Application in Plasma

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