Numerous Accurate and Stable Solitary Wave Solutions to the Generalized Modified Equal–Width Equation

Khater, Mostafa M. A.

doi:10.1007/s10773-023-05362-4

Cited by 32 publications

(1 citation statement)

References 38 publications

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“…As a result, numerous mathematicians, physicists, and engineers have developed several reliable models to carry out progressive wave approximations for these nonlinear processes and have succeeded in identifying solutions using a variety of analytical and numerical methods. Among many techniques, some efficient and powerful schemes are the new Kudryashov 12 , the generalized projective Riccati equations 13 , the extended simple equation 14 , the Bernoulli sub-ode 15 , the ( )-expansion 16 , the unified and improved F-expansion 17 , the Galarkin 18 , 19 , the Khater II 20 , the He’s variational iteration 21 , the extended Khater 22 , the direct algebraic 23 , 24 , the modified Khater 25 , the generalized rational 26 , the modified direct algebraic 27 , the novel generalized Kudryashov 28 , the extended simplest equation 29 , the generalized exponential function 30 , the Bernoulli sub-equation 31 , and various other methods. Due to this study, considerably more attention has been given to solutions, structures, interactions, and other properties of methods, and various significant results have been successfully obtained.…”

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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