A Gardner evolution equation for topographic Rossby waves and its mechanical analysis

Wang, Jie; Zhang, Ruigang; Yang, Liangui

doi:10.1016/j.amc.2020.125426

Cited by 15 publications

(6 citation statements)

References 37 publications

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“…Advances in Mathematical Physics are demonstrated through the three-dimensional and contour plots. For the solution for the generalized ZK equation with variable coefficients, Equation (26) and Equation ( 29) are of hyperbolic function type, Equation (27) and Equation ( 30) are of trigonometric function, and Equation ( 28) is of the rational type. Figure 1 represents the shock wave profile for Equation (26), and the transition of the wave is observed through the contour plots.…”

Section: Discussionmentioning

confidence: 99%

“…Similarly, Figure 2 represents the shock wave for Equation (29). Figure 3 demonstrates the multisoliton wave profile for Equation (27). Similarly, Figure 4 demonstrates the multisoliton of Equation (28).…”

Section: Discussionmentioning

confidence: 99%

“…where aðtÞ, bðtÞ, hðtÞ, gðtÞ, and f ðtÞ are smooth function of t . The Gardner equation is applied on many scientific fields such as bottom topography [24], magnetoplasma [25], plasma physics [26], mechanical analysis [27], and lattice Boltzmann model [28]. Ozkan and Yasar [29] studied the exact solutions of the nonlocal Gardner equation by employing the Hirota bilinear, extended homoclinic, and three-wave methods to obtain solutions of breather-type and multi-wave-type solitons.…”

Section: Advances In Mathematical Physicsmentioning

confidence: 99%

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Exact Solutions of the Generalized ZK and Gardner Equations by Extended Generalized $(G^{'} / G)$ -Expansion Method

Mohanty

Dev

Sahoo³

et al. 2023

Advances in Mathematical Physics

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In this investigation, the exact solutions of variable coefficients of generalized Zakharov-Kuznetsov (ZK) equation and the Gardner equation are studied with the help of an extended generalized G ′ / G expansion method. The main objective of this study is to establish the closed-form solutions and dynamics of analytical solutions to the generalized ZK equation and the Gardner equation. The generalized ZK equation and the Gardner equation govern the behavior of nonlinear wave phenomena in the presence of magnetic field in plasma dynamics, turbulence, bottom topography, and quantum field theory. We construct innovative solutions to the models under consideration using various computing tools and a recently developed extended generalized G ′ / G expansion technique. The extended generalized G ′ / G expansion technique is a well-defined and simple technique which is based on the initial assumed solutions of the polynomial of G ′ / G . The derived solutions for both the equations are the hyperbolic, trigonometric, and rational functions. The obtained solutions have shock/kink waves and multisoliton, which depict the dynamical representations of the acquired solutions through the three-dimensional surface plots and the contour plots.

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Section: Discussionmentioning

confidence: 99%

Section: Discussionmentioning

confidence: 99%

Section: Advances In Mathematical Physicsmentioning

confidence: 99%

See 1 more Smart Citation

Exact Solutions of the Generalized ZK and Gardner Equations by Extended Generalized $(G^{'} / G)$ -Expansion Method

Mohanty

Dev

Sahoo³

et al. 2023

Advances in Mathematical Physics

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“…q is the width of the waves, the values of a 1 and a 2 are related to topographic effect, meridional structure, beffect and other factors in equations ( 14), (15). It can be seen clearly that the condition for the existence of solitary waves is…”

Section: Mathematical Model and Boundary Conditionsmentioning

confidence: 99%

“…11,12 The evolution of the amplitude of the nonlinear Rossby wave under the effect of topography and dissipation satisfies the inhomogeneous Benjamin-Davis-Ono-Burgers (BDO-Burgers) equation. 13 What’s more, Yang et al 14 and Wang et al 15 derived some new equations governing the behavior of Rossby solitary waves with the effect of topography, and discussed the changes of nonlinear long wave amplitude and waveform with numerical method. Zhang et al 16 investigated the dynamics of nonlinear Rossby waves in zonally varying background current under generalized beta approximation, and the spatial-temporal slowly varying topography, which represented an unstable mechanism for the evolution of Rossby solitary waves, was a factor in linear growth or decay.…”

Section: Introductionmentioning

confidence: 99%

Forced solitary wave and vorticity with topography effect in quasi-geostrophic modelling

Zhao

Wang

2023

Advances in Mechanical Engineering

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A forced KdV equation including the special topography effect is derived to describe nonlinear long wave and solitary eddy based on the quasi-geostrophic potential vorticity model. We obtain the theoretical solution of the equation and the concrete form of stream function through perturbation theory and multi-scale analysis methods. It is found that the joint effect of weak shear basic flow and topography can change the cyclone and anticyclone structure of eddy, and in the meantime topographic structure affects the East-West propagation direction of solitary wave. Finally, according to the interaction between nonlinear long wave and topography by pseudo spectral numerical method, the topographic height is related to the amplitude, wavelength and wave velocity of the excited wave train, and the topography affects not only the spatial structure of wave, but also the amplitude of wave.

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Semi-analytical and Numerical Study on Equatorial Rossby Solitary Waves Under Non-traditional Approximation

Zhang

Liu

Yang

2022

Forum for Interdisciplinary Mathematics

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A Gardner evolution equation for topographic Rossby waves and its mechanical analysis

Cited by 15 publications

References 37 publications

Exact Solutions of the Generalized ZK and Gardner Equations by Extended Generalized $(G^{'} / G)$ -Expansion Method

Exact Solutions of the Generalized ZK and Gardner Equations by Extended Generalized $(G^{'} / G)$ -Expansion Method

Forced solitary wave and vorticity with topography effect in quasi-geostrophic modelling

Semi-analytical and Numerical Study on Equatorial Rossby Solitary Waves Under Non-traditional Approximation

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A Gardner evolution equation for topographic Rossby waves and its mechanical analysis

Cited by 15 publications

References 37 publications

Exact Solutions of the Generalized ZK and Gardner Equations by Extended GeneralizedG′/G-Expansion Method

Exact Solutions of the Generalized ZK and Gardner Equations by Extended GeneralizedG′/G-Expansion Method

Forced solitary wave and vorticity with topography effect in quasi-geostrophic modelling

Semi-analytical and Numerical Study on Equatorial Rossby Solitary Waves Under Non-traditional Approximation

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Exact Solutions of the Generalized ZK and Gardner Equations by Extended Generalized $(G^{'} / G)$ -Expansion Method

Exact Solutions of the Generalized ZK and Gardner Equations by Extended Generalized $(G^{'} / G)$ -Expansion Method