Browsing by Author "Osman, Mohamed S."

Now showing 1 - 4 of 4

Citation - WoS: 34
Citation - Scopus: 37
Abundant periodic wave solutions for fifth-order Sawada-Kotera equations
(Elsevier, 2020) Tahir, Muhammad; Awan, Aziz Ullah; Osman, Mohamed S.; Baleanu, Dumitru; Alqurashi, Maysaa M.; 56389; Matematik
In this manuscript, two nonlinear fifth-order partial differential equations, namely, the bidirectional and 2D-Sawada-Kotera equations are analytically treated using an extended form of homoclinic process. In the presence of a bilinear form, novel periodic waves with different categories including periodic soliton, solitary and kinky solitary wave solutions are constructed. In the meantime, The diverse features and mechanical qualities of these acquired solutions are elucidated by 3D figures and some contour plots.
Citation - WoS: 91
Citation - Scopus: 99
Analytical and Numerical Solutions of Mathematical Biology Models: the Newell-Whitehead-Segel and Allen-Cahn Equations
(Wiley, 2020) Inan, Bilge; Osman, Mohamed S.; Turgut, A. K.; Baleanu, Dumitru; 56389; Matematik
In this paper, we combine the unified and the explicit exponential finite difference methods to obtain both analytical and numerical solutions for the Newell-Whitehead-Segel-type equations which are very important in mathematical biology. The unified method is utilized to obtain various solitary wave solutions for these equations. Numerical solutions of the specific case studies are investigated by using the explicit exponential finite difference method ensures the accuracy and reliability of the proposed scheme. After obtaining the approximate solutions, convergence analysis and error estimation (the error norms and absolute errors) are presented by comparing these results with the analytical obtained solutions and other methods in the literature through tables and graphs. The obtained analytical and numerical results are in good agreement.
Citation - WoS: 83
Citation - Scopus: 92
Lie Symmetries, Closed-Form Solutions, and Various Dynamical Profiles of Solitons for the Variable Coefficient (2+1)-Dimensional KP Equations
(Mdpi, 2022) Kumar, Sachin; Dhiman, Shubham K.; Baleanu, Dumitru; Osman, Mohamed S.; Wazwaz, Abdul-Majid; 56389; Matematik
This investigation focuses on two novel Kadomtsev-Petviashvili (KP) equations with time-dependent variable coefficients that describe the nonlinear wave propagation of small-amplitude surface waves in narrow channels or large straits with slowly varying width and depth and non-vanishing vorticity. These two variable coefficients, Kadomtsev-Petviashvili (VCKP) equations in (2+1)-dimensions, are the main extensions of the KP equation. Applying the Lie symmetry technique, we carry out infinitesimal generators, potential vector fields, and various similarity reductions of the considered VCKP equations. These VCKP equations are converted into nonlinear ODEs via two similarity reductions. The closed-form analytic solutions are achieved, including in the shape of distinct complex wave structures of solitons, dark and bright soliton shapes, double W-shaped soliton shapes, multi-peakon shapes, curved-shaped multi-wave solitons, and novel solitary wave solitons. All the obtained solutions are verified and validated by using back substitution to the original equation through Wolfram Mathematica. We analyze the dynamical behaviors of these obtained solutions with some three-dimensional graphics via numerical simulation. The obtained variable coefficient solutions are more relevant and useful for understanding the dynamical structures of nonlinear KP equations and shallow water wave models.
Citation - WoS: 29
Citation - Scopus: 28
The general bilinear techniques for studying the propagation of mixed-type periodic and lump-type solutions in a homogenous-dispersive medium
(Amer inst Physics, 2020) Liu, Jian-Guo; Osman, Mohamed S.; Zhu, Wen-Hui; Zhou, Li; Baleanu, Dumitru; 56389; Matematik
This paper aims to construct new mixed-type periodic and lump-type solutions via dependent variable transformation and Hirota's bilinear form (general bilinear techniques). This study considers the (3 + 1)-dimensional generalized B-type Kadomtsev-Petviashvili equation, which describes the weakly dispersive waves in a homogeneous medium in fluid dynamics. The obtained solutions contain abundant physical structures. Consequently, the dynamical behaviors of these solutions are graphically discussed for different choices of the free parameters through 3D plots.