Browsing by Author "Ali Akbar, M."

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Citation - WoS: 33
Citation - Scopus: 30
Competent Closed Form Soliton Solutions To the Riemann Wave Equation and the Novikov-Veselov Equation
(Elsevier, 2020) Seadawy, Aly R.; Akbar, M. Ali; Baleanu, Dumitru; Barman, Hemonta Kumar; Ali Akbar, M.
The Riemann wave equation and the Novikov-Veselov equation are interesting nonlinear equations in the sphere of tidal and tsunami waves in ocean, river, ion and magneto-sound waves in plasmas, electromagnetic waves in transmission lines, homogeneous and stationary media etc. In this article, the generalized Kudryashov method is executed to demonstrate the applicability and effectiveness to extract travelling and solitary wave solutions of higher order nonlinear evolution equations (NLEEs) via the earlier stated equations. The technique is enucleated to extract solitary wave solutions in terms of trigonometric, hyperbolic and exponential function. We acquire bell shape soliton, consolidated bell shape soliton, compacton, singular kink soliton, flat kink shape soliton, smooth singular soliton and other types of soliton solutions by setting particular values of the embodied parameters. For the precision of the result, the solutions are graphically illustrated in 3D and 2D. The analytic solutions greatly facilitate the verification of numerical solvers on the stability analysis of the solution.
Citation - Scopus: 103
Dynamical Behavior of Solitons of the Perturbed Nonlinear Schrödinger Equation and Microtubules Through the Generalized Kudryashov Scheme
(Elsevier B.V., 2022) Wazwaz, A.-M.; Mahmud, F.; Baleanu, D.; Roy, R.; Barman, H.K.; Osman, M.S.; Ali Akbar, M.
The perturbed nonlinear Schrödinger (NLS) equation and the nonlinear radial dislocations model in microtubules (MTs) are the underlying frameworks to simulate the dynamic features of solitons in optical fibers and the functional aspects of microtubule dynamics. The generalized Kudryashov method is used in this article to extract stable, generic, and wide-ranging soliton solutions, comprising hyperbolic, exponential, trigonometric, and some other functions, and retrieve diverse known soliton structures by balancing the effects of nonlinearity and dispersion. It is established by analysis and graphs that changing the included parameters changes the waveform behavior, which is largely controlled by nonlinearity and dispersion effects. The impact of the other parameters on the wave profile, such as wave speed, wavenumber, etc., has also been covered. The results obtained demonstrate the reliability, efficiency, and capability of the implemented technique to determine wide-spectral stable soliton solutions to nonlinear evolution equations emerging in various branches of scientific, technological, and engineering domains. © 2022 The Author(s)