Browsing by Author "Wazwaz, Abdul-Majid"

Now showing 1 - 2 of 2

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: 35
Citation - Scopus: 42
Protracted study on a real physical phenomenon generated by media inhomogeneities
(Elsevier, 2021) Almusawa, Hassan; Ali, Khalid K.; Wazwaz, Abdul-Majid; Mehanna, M. S.; Baleanu, D.; Osman, M. S.; 56389; Matematik
In this work, we study the dynamical behavior for a real physical application due to the inhomogeneities of media via analytical and numerical approaches. This phenomenon is described by the 3D Date-Jimbo-Kashiwara-Miwa (3D-DJKM) equation. For analytical techniques, three different methods are performed to get hyperbolic, trigonometric and rational functions solutions. After that, the obtained solutions are graphically depicted through 2D-and 3D-plots and numerically compared via the finite difference algorithm to check the precision of the proposed methods.