ALY R SEADAWY
Articles written in Pramana – Journal of Physics
Volume 87 Issue 2 August 2016 Article ID 0020 Research Article
Nonlinear Rayleigh--Taylor instability of the cylindrical fluid flow with mass and heat transfer
The nonlinear Rayleigh--Taylor stability of the cylindrical interface between the vapour and liquid phases of a fluid is studied. The phases enclosed between two cylindrical surfaces coaxial with mass and heat transfer is derived from nonlinear Ginzburg--Landau equation. The F-expansion method is used to get exactsolutions for a nonlinear Ginzburg--Landau equation. The region of solutions is displayed graphically.
Volume 89 Issue 3 September 2017 Article ID 0049 Research Article
Nonlinear two-dimensional Kadomtsev–Petviashvili (KP) equation governs the behaviour of nonlinear waves in dusty plasmas with variable dust charge and two temperature ions. By using the reductive perturbation method, the two-dimensional dust-acoustic solitary waves (DASWs) in unmagnetized cold plasma consisting of dust fluid, ions and electrons lead to a KP equation. We derived the solitary travelling wave solutions of the twodimensional nonlinear KP equation by implementing sech–tanh, sinh–cosh, extended direct algebraic and fraction direct algebraicmethods. We found the electrostatic field potential and electric field in the form travellingwave solutions for two-dimensional nonlinear KP equation. The solutions for the KP equation obtained by using these methods can be demonstrated precisely and efficiency. As an illustration, we used the readymade package of $\it{Mathematica}$ program 10.1 to solve the original problem. These solutions are in good agreement with the analytical one.
Volume 90 Issue 5 May 2018 Article ID 0059 Research Article
MOSTAFA M A KHATER ALY R SEADAWY DIANCHEN LU
In this research, we apply two different techniques on nonlinear complex fractional nonlinear Schrödinger equation which is a very important model in fractional quantum mechanics. Nonlinear Schrödinger equation is one of the basic models in fibre optics and many other branches of science. We use the conformable fractional derivative to transfer the nonlinear real integer-order nonlinear Schrödinger equation to nonlinear complex fractional nonlinear Schrödinger equation. We apply new auxiliary equation method and novel $(G^{'} / G)$-expansion method on nonlinear complex fractional Schrödinger equation to obtain new optical forms of solitary travelling wave solutions. We find many new optical solitary travelling wave solutions for this model. These solutions are obtained precisely and efficiency of the method can be demonstrated.
Volume 91 Issue 2 August 2018 Article ID 0026 Research Article
ABDULLAH ALY R SEADAWY JUN WANG
Propagation of three-dimensional nonlinear ion-acoustic solitary waves and shocks in a homogeneous magnetised electron–positron–ion plasma is analysed. Modified extended mapping method is introduced to find ion-acoustic solitary wave solutions of the three-dimensional modified Korteweg–de Vries–Zakharov–Kuznetsov equation. As a result, solitary wave solutions (which represent electrostatic field potential), electric fields, magneticfields and quantum statistical pressures are obtained with the aid of Mathematica. These new exact solitary wave solutions are obtained in different forms such as periodic, kink and antikink, dark soliton, bright soliton, bright and dark solitary wave etc. The results are expressed in the forms of hyperbolic, trigonometric, exponential and rational functions. The electrostatic field potential and electric and magnetic fields are shown graphically. Theseresults demonstrate the efficiency and precision of the method that can be applied to many other mathematical and physical problems.
Volume 91 Issue 4 October 2018 Article ID 0048 Research Article
MUHAMMAD NASIR ALI ALY R SEADAWY SYED MUHAMMAD HUSNINE
In this study, we explore the modified form of (1 + n)-dimensional Zakharov–Kuznetsov equation, which is used to investigate the waves in dusty and magnetised plasma. It is proved that the equation follows the property of nonlinear self-adjointness. Lie point symmetries are calculated and conservation laws in the framework of the new general conservation theorem of Ibragimov are obtained. The $(1/G'), (G'/G)$-expansion and modified Kudryshov methods are applied to extract exact analytical solutions. The so-called bright, dark and singular solutions are also found using the solitary wave ansatz method. The results obtained in this study are new and may be of significant importance where this model is used to study the waves in different plasmas.
Volume 91 Issue 5 November 2018 Article ID 0068 Research Article
KALIM U TARIQ ALY R SEADAWY SULTAN Z ALAMRI
In this paper, the auxiliary equation method is successfully applied to compute analytical solutions for (3+1)-dimensional generalised Kadomtsev–Petviashvili and (2+1)-dimensional Gardner–Kadomtsev–Petviashvili equations, by introducing simple transformations. These results hold numerous travelling wave solutions that areof key importance which provide a powerful mathematical tool for solving nonlinear wave equations in recent era of applied science and engineering. The method can also be extended to other nonlinear evolution models arisingin contemporary physics.
Volume 92 Issue 6 June 2019 Article ID 0088 Research Article
Structure of system solutions of ion sound and Langmuir dynamical models and their applications
ALY R SEADAWY ASGHAR ALI DIANCHEN LU
The present study deals with the system of equations for the ion sound and Langmuir waves (SEISLWs) by employing the extended simple equation, modified F-expansion and exp($−\Psi(\xi)$) expansion methods for constructing novel exact travelling wave solutions. Graphical simulations of some solutions are helpful to study the behaviour of SEISLWs. Hence, this approach is practically effective and productive to better understand the nonlinear problems in mathematics, physics and engineering.
Volume 93 Issue 1 July 2019 Article ID 0010 Research Article
ALY R SEADAWY DIANCHEN LU MUJAHID IQBAL
We investigated the new exact travelling wave solutions of the system of equations for the ion sound and Langmuir waves (SEISLWs). In this work, we use the extended form of two methods, auxiliary equation mapping and direct algebraic methods, to find the families of new exact travelling wave solutions of the SEISLWs. These new exact travelling solutions are derived in the form of trigonometric functions, hyperbolic functions, periodic solitary waves, bright and dark solitons, kink solutions of the SEISLWs.We used the Mathematica program to show these solutions in two and three dimensions graphically.
Volume 93 Issue 3 September 2019 Article ID 0044 Research Article
DIANCHEN LU ALY R SEADAWY JUN WANG MUHAMMAD ARSHAD UMER FAROOQ
The generalised nonlinear Schrödinger equation (NLSE) of third order is investigated, which accepts one-hump embedded solitons in a single-parameter family. In this paper, we constructed analytical solutions in the form of solitary waves and solitons of third-order NLSE by employing the extended simple equation method and exp($−\Phi(\xi)$)-expansion method. In applied physics and engineering, the obtained exact solutions have important applications. The stability of the model is examined by employing modulational instability which verifies that all the achieved exact solutions are stable. The movements of exact solitons are also presented graphically, which assist the researchers to know the physical interpretation of this complex model. Several such types of problems arising in engineering and physics can be resolved by utilising these reliable, influential and effective methods.
Volume 94 All articles Published: 1 January 2020 Article ID 0017 Research Article
ALY R SEADAWY DAVID YARO DIANCHEN LU
This work applies the modified extended direct algebraic method to construct some novel exact travelling wave solutions for the coupled (2 + 1)-dimensional Konopelchenko–Dubrovsky (KD) equation. Soliton, periodic, solitary wave, Jacobi elliptic function, new elliptic, Weierstrass elliptic function solutions and so on are obtained, which have several implementations in the field of applied sciences and engineering. In addition, we discuss the dynamics of some solutions like periodic, soliton and dark-singular combo soliton by their evolutionary shapes.
Volume 94, 2020
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