Viewing the Solar System via a variable-coefficient nonlinear dispersive-wave system

Gao, Xin-Yi; Guo, Yong-Jiang; Shan, Wen-Rui

doi:10.1007/s00707-020-02747-y

Cited by 24 publications

(3 citation statements)

References 58 publications

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“…Figure 4 shows the numerical domain and structured meshes with 785,000 elements for inside and outside the fluidic oscillator. Many researchers have tried to solve the nonlinear mathematical equations in physics to describe many physical phenomena [24][25][26][27][28][29]. The Navier-Stokes equations are non-linear partial differential equations, which describe the motion of viscous fluid substances, and they Fig.…”

Section: Grid Generation and Numerical Methodsmentioning

confidence: 99%

Flow features of a new fluidic oscillator using time-resolved PIV measurement and 3D numerical simulation

et al. 2021

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The current study measures the instantaneous velocity field inside and outside a new designed fluidic oscillator using planar time-resolved PIV technique on its symmetry plane in a water tank. The instantaneous velocity field showed that the interaction of four vortices with the jet was the main reason of jet oscillation inside the main chamber. Threedimensional transient numerical solutions were also carried out using Ansys-Fluent 2020R2 software. Four turbulence models (k-ε, k-ε RNG, k-ω, and k-ω SST) were used for these numerical solutions, which their results were then compared with the PIV results, qualitatively and quantitatively. The comparison showed that the k-ε and k-ω SST models were better for simulating the flow of the new oscillator. However, both models over-predicted the jet spreading angle and oscillation frequency compared to the PIV results. A similar PIV measurement was accomplished outside the conventional oscillator to compare the timeaveraged velocity fields of the new and conventional oscillators. The comparison showed that the amplitude and frequency of the new oscillator were, respectively, lower and higher than those of the conventional one. The time-averaged velocity and momentum flux outside the new oscillator was significantly higher than for the conventional one. Abbreviations A Throat area (m 2 ) D Throat height (m) D h Hydraulic diameter (m) Fr Oscillation frequency (1/s) f Oscillation frequency (1/s) H Domain height outside the oscillator (m) rate k Turbulence kinetic energy (m 2 /s 2

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Section: Grid Generation and Numerical Methodsmentioning

confidence: 99%

Flow features of a new fluidic oscillator using time-resolved PIV measurement and 3D numerical simulation

et al. 2021

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“…It is pertinent to note here that Burgers system, with the proper choice of the parameters involved, can be shown to be similar to the well-known incompressible Navier-Stokes equations excluding the pressure and continuity that can be used in the models for studying hydrodynamical turbulence and wave processes in non-linear media [4] . Gao et al [4] worked out on hetero-Bäcklund (non-auto-Bäcklund) transformation for an extended (2+1)-D coupled Burgers system in fluid mechanics, whereas Gao et al [5] , [32] , [33] worked out on the auto- and non-auto-Bäcklund transformations for a higher-order Boussinesq-Burgers system, a generalized (2+1)-D dispersive long-wave system, and a variable-coefficient nonlinear dispersive-wave system, respectively, for studying oceanic waves including the Earth, Enceladus, and Titan.…”

Section: Introductionmentioning

confidence: 99%

Lump, lump-stripe, and breather wave solutions to the (2 + 1)-dimensional Sawada-Kotera equation in fluid mechanics

Ali

Bilkis²,

Paul

et al. 2021

Heliyon

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The present study investigates the lump, one-stripe, lump-stripe, and breather wave solutions to the (2+1)-dimensional Sawada-Kotera equation using the Hirota bilinear method. For lump and lump-stripe solutions, a quadratic polynomial function, and a quadratic polynomial function in conjunction with an exponential term are assumed for the unknown function f giving the solution to the mentioned equation, respectively. On the other hand, only an exponential function is considered for one-stripe solutions. Besides, the homoclinic test approach is adopted for constructing breather wave solutions. The propagations of the attained lump, lump-stripe, and breather wave solutions are shown through some graphical illustrations. The graphical outputs demonstrate that the lump wave moves along the straight line and exponentially decreases away from the origin of the spatial domain. On the other hand, lump-kink solutions illustrate the fission and fusion interaction behaviors upon the selection of the free parameters. Fission and fusion processes show that the stripe soliton splits into a stripe soliton and a lump soliton, and then the lump soliton merges into one stripe soliton. In addition, the achieved breather waves illustrate the periodic behaviors in the xy -plane. The outcomes of the study can be useful for a better understanding of the physical nature of long waves in shallow water under gravity.

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“…In recent years, the investigation of analytic travelling wave solutions of nonlinear partial differential equations (NPDEs) has been the concern of researchers who are involved in carrying out studies on the way to secure closed-form solutions of NPDEs that evolve from nonlinear phenomena [2][3][4][5][6]. These phenomena can be found in numerous fields of research including structured or methodical works in chemical kinematics, optical fibres, engineering, solid-state physics, oceanic, biology as well as meteorology [7][8][9][10][11][12][13].…”

Section: Introductionmentioning

confidence: 99%

Soliton solutions, travelling wave solutions and conserved quantities for a three-dimensional soliton equation in plasma physics

Khalique¹,

Adeyemo²

2021

Commun. Theor. Phys.

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Many physical systems can be successfully modelled using equations that admit the soliton solutions. In addition, equations with soliton solutions have a significant mathematical structure. In this paper, we study and analyze a three-dimensional soliton equation, which has applications in plasma physics and other nonlinear sciences such as fluid mechanics, atomic physics, biophysics, nonlinear optics, classical and quantum fields theories. Indeed, solitons and solitary waves have been observed in numerous situations and often dominate long-time behaviour. We perform symmetry reductions of the equation via the use of Lie group theory and then obtain analytic solutions through this technique for the very first time. Direct integration of the resulting ordinary differential equation is done which gives new analytic travelling wave solutions that consist of rational function, elliptic functions, elementary trigonometric and hyperbolic functions solutions of the equation. Besides, various solitonic solutions are secured with the use of a polynomial complete discriminant system and elementary integral technique. These solutions comprise dark soliton, doubly-periodic soliton, trigonometric soliton, explosive/blowup and singular solitons. We further exhibit the dynamics of the solutions with pictorial representations and discuss them. In conclusion, we contemplate conserved quantities for the equation under study via the standard multiplier approach in conjunction with the homotopy integral formula. We state here categorically and emphatically that all results found in this study as far as we know have not been earlier obtained and so are new.

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Viewing the Solar System via a variable-coefficient nonlinear dispersive-wave system

Cited by 24 publications

References 58 publications

Flow features of a new fluidic oscillator using time-resolved PIV measurement and 3D numerical simulation

Flow features of a new fluidic oscillator using time-resolved PIV measurement and 3D numerical simulation

Lump, lump-stripe, and breather wave solutions to the (2 + 1)-dimensional Sawada-Kotera equation in fluid mechanics

Soliton solutions, travelling wave solutions and conserved quantities for a three-dimensional soliton equation in plasma physics

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Viewing the Solar System via a variable-coefficient nonlinear dispersive-wave system

Cited by 24 publications

References 58 publications

Flow features of a new fluidic oscillator using time-resolved PIV measurement and 3D numerical simulation

Flow features of a new fluidic oscillator using time-resolved PIV measurement and 3D numerical simulation

Lump, lump-stripe, and breather wave solutions to the (2 + 1)-dimensional Sawada-Kotera equation in fluid mechanics

Soliton solutions, travelling wave solutions and conserved quantities for a three-dimensional soliton equation in plasma physics

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Lump, lump-stripe, and breather wave solutions to the (2 + 1)-dimensional Sawada-Kotera equation in fluid mechanics