Wave solitons to a nonlinear doubly dispersive equation in describing the nonlinear wave propagation via two analytical techniques

Alharthi, Mohammed Shaaf

doi:10.1016/j.rinp.2023.106362

Cited by 3 publications

(2 citation statements)

References 43 publications

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“…Their work focused on exploring various solutions, particularly single-wave propagation patterns derived from the proposed model. Alharthi et al 38 have examined wave solutions of the DD model using the modified generalized exponential rational function method and the Jacobi elliptical finder method. Rehman et al 39 investigated wave solutions of the DD model, which characterizes nonlinear wave propagation in the EIMR, employing the Sardar sub-equation method.…”

Section: Introductionmentioning

confidence: 99%

Bifurcation analysis and soliton solutions to the doubly dispersive equation in elastic inhomogeneous Murnaghan’s rod

Islam

2024

Sci Rep

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The doubly dispersive (DD) equation finds extensive utility across scientific and engineering domains. It stands as a significant nonlinear physical model elucidating nonlinear wave propagation within the elastic inhomogeneous Murnaghan’s rod (EIMR). With this in mind, we have focused on the integration of the DD model and the modified Khater (MK) method. Through the wave transformation, this model is effectively converted into an ordinary differential equation. In this paper, the goal of our work is to explore new wave solutions to the DD model by using the MK scheme. These solutions provide extremely helpful insights into the operation of the system. The three-dimensional (3D) plot and two-dimensional (2D) combined plot via the impacts of the parameters are provided for various parameters in this manuscript. We also discussed the dynamical properties of the model, which are accomplished through the bifurcation analysis, and also found the Hamiltonian function. This research makes a substantial contribution to the area by increasing our understanding of wave solutions in the DD, introducing novel investigation tools, and carrying out an in-depth investigation of the bifurcation and stability aspects of the system. As a direct result of this research, novel openings have been uncovered for further investigation and application in the various disciplines of science and engineering.

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Section: Introductionmentioning

confidence: 99%

Bifurcation analysis and soliton solutions to the doubly dispersive equation in elastic inhomogeneous Murnaghan’s rod

Islam

2024

Sci Rep

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“…Their work focused on exploring various solutions, particularly single-wave propagation patterns derived from the proposed model. Alharthi et al [20] examined soliton solutions of the DDE model using the modified generalized exponential rational function method and the Jacobi elliptical finder method.…”

Section: Introductionmentioning

confidence: 99%

Bifurcation analysis of the soliton solutions to the Doubly dispersive equation in elastic inhomogeneous Murnaghan’s rod

Rayhanul

2023

Preprint

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The Doubly Dispersive Equation (DDE) finds extensive utility across scientific and engineering domains. It stands as a significant nonlinear physical model elucidating nonlinear wave propagation within the elastic inhomogeneous Murnaghan’s rod (EIMR). With this in mind, we have focused on the integration of the DDE model and the advanced auxiliary equation (AAM) scheme. Through wave transformation, this model is effectively converted into an ordinary differential equation. In this paper, the goal of our work is to explore new wave solutions of the DDE model by using AAE scheme, which solutions are extremely helpful insights into the operation of the system. The impacts of the parameters are provided in this manuscript. We also discussed about the dynamical properties of the model, which is accomplished through bifurcation and stability investigations and also found the Hamiltonian function. This research makes a substantial contribution to the area by increasing our understanding of soliton solutions in the DDE, introducing novel investigation tools, and carrying out an in-depth investigation of the bifurcation and stability aspects of the system. As a direct result of this research, novel openings have been uncovered for further investigation and application in the various disciplines of science and engineering.

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Further quality analytical investigation on soliton solutions of some nonlinear PDEs with analyses: Bifurcation, sensitivity, and chaotic phenomena

Chowdhury,

Miah,

Rasid

et al. 2024

Alexandria Engineering Journal

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Wave solitons to a nonlinear doubly dispersive equation in describing the nonlinear wave propagation via two analytical techniques

Cited by 3 publications

References 43 publications

Bifurcation analysis and soliton solutions to the doubly dispersive equation in elastic inhomogeneous Murnaghan’s rod

Bifurcation analysis and soliton solutions to the doubly dispersive equation in elastic inhomogeneous Murnaghan’s rod

Bifurcation analysis of the soliton solutions to the Doubly dispersive equation in elastic inhomogeneous Murnaghan’s rod

Further quality analytical investigation on soliton solutions of some nonlinear PDEs with analyses: Bifurcation, sensitivity, and chaotic phenomena

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