Browsing by Author "Rezazadeh, Hadi"

Now showing 1 - 8 of 8

Citation - WoS: 33
Citation - Scopus: 34
Application of Modified Extended Tanh Technique for Solving Complex Ginzburg-Landau Equation Considering Kerr Law Nonlinearity
(Tech Science Press, 2021) Shallal, Muhannad A.; Mirhosseini-Alizamini, Seyed Mehdi; Rezazadeh, Hadi; Javeed, Shumaila; Baleanu, Dumitru; Chu, Yuming; 56389; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
The purpose of this work is to find new soliton solutions of the complex Ginzburg-Landau equation (GLE) with Kerr law non-linearity. The considered equation is an imperative nonlinear partial differential equation (PDE) in the field of physics. The applications of complex GLE can be found in optics, plasma and other related fields. The modified extended tanh technique with Riccati equation is applied to solve the Complex GLE. The results are presented under a suitable choice for the values of parameters. Figures are shown using the three and two-dimensional plots to represent the shape of the solution in real, and imaginary parts in order to discuss the similarities and difference between them. The graphical representation of the results depicts the typical behavior of soliton solutions. The obtained soliton solutions are of different forms, such as, hyperbolic and trigonometric functions. The results presented in this paper are novel and reported first time in the literature. Simulation results establish the validity and applicability of the suggested technique for the complex GLE. The suggested method with symbolic computational software such as, Mathematica and Maple, is proven as an effective way to acquire the soliton solutions of nonlinear partial differential equations (PDEs) as well as complex PDEs.
Citation - WoS: 4
Citation - Scopus: 5
Ginzburg Landau Equation's Innovative Solution (Gleis)
(Iop Publishing Ltd, 2021) Rezazadeh, Hadi; Baleanu, Dumitru; Desta Leta, Temesgen; Javeed, Shumaila; Alimgeer, Khurram Saleem; El Achab, Abdelfattah; 56389; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
A novel soliton solution of the famous 2D Ginzburg-Landau equation is obtained. A powerful Sine-Gordon expansion method is used for acquiring soliton solutions 2D Ginzburg-Landau equation. These solutions are obtained with the help of contemporary software (Maple) that allows computation of equations within the symbolic format. Some new solutions are depicted in the forms of figures. The Sine-Gordon method is applicable for solving various non-linear complex models such as, Quantum mechanics, plasma physics and biological science.
Citation - WoS: 34
Citation - Scopus: 33
New Optical Solitons of Conformable Resonant Nonlinear Schrodinger's Equation
(de Gruyter Poland Sp Z O O, 2020) Rezazadeh, Hadi; Abazari, Reza; Khater, Mostafa M. A.; Inc, Mustafa; Baleanu, Dumitru; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
Sardar subequation approach, which is one of the strong methods for solving nonlinear evolution equations, is applied to conformable resonant Schrodinger's equation. In this technique, if we choose the special values of parameters, then we can acquire the travelling wave solutions. We conclude that these solutions are the solutions obtained by the first integral method, the trial equation method, and the functional variable method. Several new traveling wave solutions are obtained including generalized hyperbolic and trigonometric functions. The new derivation is of conformable derivation introduced by Atangana recently. Solutions are illustrated with some figures.
Citation - WoS: 175
Citation - Scopus: 183
New Solitary Wave Solutions for Variants of (3+1)-Dimensional Wazwaz-Benjamin Equations
(Frontiers Media Sa, 2020) Inc, Mustafa; Baleanu, Dumitru; Rezazadeh, Hadi; 56389; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
We solve distinct forms of (3+1)-Dimensional Wazwaz-Benjamin-Bona-Mahony [(3+1)-Dimensional WBBM] equations by employing the method of Sardar-subequation. When parameters involving this approach are taken to be special values, we can obtain the solitary wave solutions (sws) which is concluded from other approaches such as the functional variable method, the trail equation method, the first integral method and so on. We obtain new and general solitary wave solutions in terms of generalized hyperbolic and trigonometric functions. The results demonstrate the power of the proposed method for the determination of sws of non-linear evolution equations (NLEs).
Citation - WoS: 10
Citation - Scopus: 12
Soliton Solutions for Non-Linear Kudryashov's Equation Via Three Integrating Schemes
(Vinca inst Nuclear Sci, 2021) Mirhosseini-Alizamini, Mehdi; Baleanu, Dumitru; Rezazadeh, Hadi; Inc, Mustafa; Hussain, Majid; Arshed, Saima; 56389; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
This paper considers the non-linear Kudryashov's equation, that is an extension of the well-known dual-power law of refractive index and is analog to the generalized version of anti-cubic non-linearity. The model is considered in the presence of full non-linearity. The main objective of this paper is to extract soliton solutions of the proposed model. Three state-of-the-art integration schemes, namely modified auxiliary equation method, the sine-Gordon expansion method and the tanh-coth expansion method have been employed for obtaining the desired soliton solutions.
Citation - WoS: 12
Citation - Scopus: 16
Soliton Solutions of Nonlinear Boussinesq Models Using the Exponential Function Technique
(Iop Publishing Ltd, 2021) Baleanu, Dumitru; Nawaz, Sidra; Rezazadeh, Hadi; Javeed, Shumaila; 56389; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
This paper deals with the new analytical solutions of conformable nonlinear Boussinesq equations. Boussinesq equation is one of the important equation in the field of applied mathematics and engineering, particularly in optical fibers, plasma physics, fluid dynamics, signal processing, and shallow water etc. The focus of this paper is to obtain the new explicit solutions of conformable Boussinesq equations. Exponential function technique is employed to solve the considered models. The conformable properties are utilized to obtain new analytical solutions for this type of nonlinear Boussinesq equations. The new analytical solutions are acquired especially for the space-time boussinesq equation. The results are shown graphically. The obtained solutions can be useful for engineers and physicists to further analyze the phenomena. The implemented technique is valuable for finding new analytical solutions of nonlinear partial differential equations (PDEs).
Solitons of the (1 + 1) - and (2 + 1) -Dimensional Chiral Nonlinear Schrodinger Equations with the Jacobi Elliptical Function Method
(2023) Tala-Tebue, Eric; Rezazadeh, Hadi; Javeed, Shumaila; Baleanu, Dumitru; Korkmaz, Alper; 56389; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
Our objective is to find new analytical solutions of the (1 + 1) - and (2 + 1) -dimensional Chiral nonlinear Schrodinger (CNLS) equations using the Jacobi elliptical function method. The CNLS equations play a significant role in the development of quantum mechanics, particularly in the field of quantum Hall effect. Soliton solutions of the considered models are obtained such as, cnoidal solutions, the hyperbolic solutions and the trigonometric solutions. The obtained analytical solutions are new in the literature. The stability conditions of these solutions are also given. The obtained stable solutions are presented graphically for some specific parameters. Moreover, the conditions of modulational instability for both models are provided. The proposed method can be useful to obtain the analytical solutions of nonlinear partial differential equations.
Citation - WoS: 9
Citation - Scopus: 10
Solitons of the (1+1)- and (2+1)-Dimensional Chiral Nonlinear Schrodinger Equations With the Jacobi Elliptical Function Method
(Springer Basel Ag, 2023) Rezazadeh, Hadi; Javeed, Shumaila; Baleanu, Dumitru; Korkmaz, Alper; Tala-Tebue, Eric; 56389; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
Our objective is to find new analytical solutions of the (1+1)- and (2+1)-dimensional Chiral nonlinear Schrodinger (CNLS) equations using the Jacobi elliptical function method. The CNLS equations play a significant role in the development of quantum mechanics, particularly in the field of quantum Hall effect. Soliton solutions of the considered models are obtained such as, cnoidal solutions, the hyperbolic solutions and the trigonometric solutions. The obtained analytical solutions are new in the literature. The stability conditions of these solutions are also given. The obtained stable solutions are presented graphically for some specific parameters. Moreover, the conditions of modulational instability for both models are provided. The proposed method can be useful to obtain the analytical solutions of nonlinear partial differential equations.