Asymptotic properties of solutions of third-order nonlinear dynamic equations on time scales

Saker, S. H.; Hassan, Haydir Ali

doi:10.22436/jmcs.026.03.05

Cited by 2 publications

(2 citation statements)

References 21 publications

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“…Climate change and global warming are examples of these great natural disasters. Flooding, heat waves, early spring arrival, sea-level rise, glacier melting, coral reef bleaching, and disease contagions are the present-day results of climate change [3][4][5][6][7]. Nevertheless, these giant waves can constitute alternative energy resources for near-future applications if the essential technology is implemented [8][9][10][11][12].…”

Section: Introductionmentioning

confidence: 99%

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Solitary Wave Propagation of the Generalized Rosenau–Kawahara–RLW Equation in Shallow Water Theory with Surface Tension

AL-saedi,

Nikan,

Avazzadeh

et al. 2023

Symmetry

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This paper addresses a numerical approach for computing the solitary wave solutions of the generalized Rosenau–Kawahara–RLW model established by coupling the generalized Rosenau–Kawahara and Rosenau–RLW equations. The solution of this model is accomplished by using the finite difference approach and the upwind local radial basis functions-finite difference. Firstly, the PDE is transformed into a nonlinear ODEs system by means of the radial kernels. Secondly, a high-order ODE solver is implemented for discretizing the system of nonlinear ODEs. The main advantage of this technique is its lack of need for linearization. The global collocation techniques impose a significant computational cost, which arises from calculating the dense system of algebraic equations. The proposed technique estimates differential operators on every stencil. As a result, it produces sparse differentiation matrices and reduces the computational burden. Numerical experiments indicate that the method is precise and efficient for long-time simulation.

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Section: Introductionmentioning

confidence: 99%

“…In order to take nonlinear waves into consideration, Pan and He [28] derived the Rosenau-Kawahara equation with the addition of the viscous terms −u xxxxx and +u xxx and obtained the generalized form of the Rosenau-RLW model (3). They investigated the solitary and periodic solutions of the following equation:…”

Section: Introductionmentioning

confidence: 99%

Solitary Wave Propagation of the Generalized Rosenau–Kawahara–RLW Equation in Shallow Water Theory with Surface Tension

AL-saedi,

Nikan,

Avazzadeh

et al. 2023

Symmetry

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New precise solutions to the Bogoyavlenskii equation by extended rational techniques

Karchi

Ghaemi

Vahidi

2023

Int. J. Mod. Phys. B

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This paper adopts the rational extended sine-cosine and cosh-sinh methods to construct the Bogoyavlenskii equation’s exact solutions. To the best of our knowledge, the Bogoyavlenskii equation has not been investigated by aforementioned techniques. In this paper, we find the precise traveling wave solutions of the Bogoyavlenskii equation. Finally, 3D and 2D graphics of the obtained solutions are illustrated for the applicability and reliability of the proposed strategy for various special values.

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Asymptotic properties of solutions of third-order nonlinear dynamic equations on time scales

Abstract: This paper is concerned with the asymptotic properties of solutions of third-order nonlinear dynamic equations on time scales. Some sufficient conditions for oscillation and nonoscillation of solutions as well as the boundedness of the solutions are established.

Cited by 2 publications

References 21 publications

Solitary Wave Propagation of the Generalized Rosenau–Kawahara–RLW Equation in Shallow Water Theory with Surface Tension

Solitary Wave Propagation of the Generalized Rosenau–Kawahara–RLW Equation in Shallow Water Theory with Surface Tension

New precise solutions to the Bogoyavlenskii equation by extended rational techniques

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