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

Fu, Lei; Chen, Yaodeng; Yang, Hongwei

doi:10.3390/math7010041

Cited by 32 publications

(17 citation statements)

References 59 publications

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“…Substituting equations (12) and (13) into equation 11, we can obtain the governing equation and the boundary condition of u(z)…”

Section: Derivation Of the 2d Bo Equationmentioning

confidence: 99%

Two-dimensional fractional algebraic internal solitary waves model and its solution

Chen

et al. 2019

Advances in Mechanical Engineering

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With the development of theory and advancement of scientific research, fractional calculus has begun to be considered as a method for the study of physical systems. In this work, based on the basic system of equations for internal solitary waves, we have derived two-dimensional Benjamin-Ono equation. Then, the integer-order two-dimensional Benjamin-Ono equation is transformed into the time-fractional Benjamin-Ono equation. To study the properties of the algebraic internal solitary waves, we discuss the conservation laws of the new model. Also, using the Hirota bilinear method, the derived new model is solved. Finally, we explore the characteristics of motion of the algebraic internal solitary waves with the help of the multi-soliton solutions.

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“…Substituting equations (12) and (13) into equation 11, we can obtain the governing equation and the boundary condition of u(z)…”

Section: Derivation Of the 2d Bo Equationmentioning

confidence: 99%

Two-dimensional fractional algebraic internal solitary waves model and its solution

Chen

et al. 2019

Advances in Mechanical Engineering

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“…So far, many scholars have obtained significant results for chemostat models [1][2][3][4][5][6][7][8][9][10][11]. While the populations in nature suffer from instantaneous discontinuous interference (for example, toxic input, seasonal harvest, and spraying pesticides), this interference phenomenon can be described as an impulse mathematically [12][13][14][15][16]. Furthermore, the theory and method of impulsive differential equations are widely used in many domains of biological science [17][18][19][20].…”

Section: Introductionmentioning

confidence: 99%

Dynamics of an Impulsive Stochastic Nonautonomous Chemostat Model with Two Different Growth Rates in a Polluted Environment

Meng

2019

Discrete Dynamics in Nature and Society

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This paper proposes a novel impulsive stochastic nonautonomous chemostat model with the saturated and bilinear growth rates in a polluted environment. Using the theory of impulsive differential equations and Lyapunov functions method, we first investigate the dynamics of the stochastic system and establish the sufficient conditions for the extinction and the permanence of the microorganisms. Then we demonstrate that the stochastic periodic system has at least one nontrivial positive periodic solution. The results show that both impulsive toxicant input and stochastic noise have great effects on the survival and extinction of the microorganisms. Furthermore, a series of numerical simulations are presented to illustrate the performance of the theoretical results.

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“…For a long time, people have been committed to the study of integral calculus. Therefore, researchers conduct scientific research based on integer order models [13][14][15][16][17][18]. However, with the continuous development of calculus theory, the appearance and development of fractional order have become a major trend of integral science [19][20][21].…”

Section: Introductionmentioning

confidence: 99%

An Application of (3+1)-Dimensional Time-Space Fractional ZK Model to Analyze the Complex Dust Acoustic Waves

Yang

2019

Complexity

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Dust plasma is a new field of physics which has developed rapidly in recent decades. The study of dust plasma has received much attention due to its importance in the environment of space and the Earth. Dust acoustic waves are generated because of the inertia of dust mass while the restoring force is provided by the thermal pressure of electrons and ions. Since dust acoustic waves were first reported theoretically in unmagnetized dust plasma by Rao et al., they have become a research hot spot. In this paper, the excitation of dust acoustic waves by a gravity field in a dust plasma is analyzed. According to the control equations of dust plasma motion and employing multiscale analysis and perturbation method, we have obtained a (3+1)-dimensional ZK model. Because of the space property of dust plasma, (3+1)-dimensional ZK equation is more suitable than KdV equation and (2+1)-dimensional ZK equation to describe the real dust acoustic waves. Then, the (3+1)-dimensional time-space fractional ZK (TSF-ZK) equation describing the fractal process of nonlinear dust acoustic waves is given for the first time. To further explore how dust acoustic waves change energy as they travel, we discuss the conservation laws of the new model. Moreover, we study the exact solution of (3+1)-dimensional TSF-ZK equation by using extended Kudryashov method. Finally, based on the exact solution, we further investigate the effect of the parameter k, the charge properties of dust particle Zd0, the fractional order values α, β, γ, and θ, the temperature Td, the gravity g, and the collision frequency β0 and β1 on the properties of dust acoustic waves by a gravity field in dust plasma.

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

Cited by 32 publications

References 59 publications

Two-dimensional fractional algebraic internal solitary waves model and its solution

Two-dimensional fractional algebraic internal solitary waves model and its solution

Dynamics of an Impulsive Stochastic Nonautonomous Chemostat Model with Two Different Growth Rates in a Polluted Environment

An Application of (3+1)-Dimensional Time-Space Fractional ZK Model to Analyze the Complex Dust Acoustic Waves

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