Browsing by Author "Mirzazadeh, Mohammad"

Now showing 1 - 9 of 9

Citation Count: Samavat, Majid;...et.al. (2022). "A New (4 + 1)-Dimensional Burgers Equation: Its Bäcklund Transformation and Real and Complex -Kink Solitons", International Journal of Applied and Computational Mathematics, Vol.8, No.172.
A New (4 + 1)-Dimensional Burgers Equation: Its Bäcklund Transformation and Real and Complex -Kink Solitons
(2022) Samavat, Majid; Mirzazadeh, Mohammad; Hosseini, Kamyar; Salahshour, Soheil; Baleanu, Dumitru; 56389
Studying the dynamics of solitons in nonlinear evolution equations (NLEEs) has gainedconsiderable interest in the last decades. Accordingly, the search for soliton solutions ofNLEEs has been the main topic of many research studies. In the present paper, a new (4+ 1)-dimensional Burgers equation (n4D-BE) is introduced that describes speciﬁc disper-sive waves in nonlinear sciences. Based on the truncated Painlevé expansion, the Bäcklundtransformation of the n4D-BE is ﬁrstly extracted, then, its real and complex N-kink solitonsare derived using the simpliﬁed Hirota method. Furthermore, several ansatz methods areformally adopted to obtain a group of other single-kink soliton solutions of the n4D-BE
Citation Count: Hosseini, Kamyar...et al. (2021). "An analytic study on the approximate solution of a nonlinear time-fractional Cauchy reaction-diffusion equation with the Mittag-Leffler law", Mathematical Methods in the Applied Sciences, Vol. 44, no. 8, pp. 6247-6258.
An analytic study on the approximate solution of a nonlinear time-fractional Cauchy reaction-diffusion equation with the Mittag-Leffler law
(2021) Hosseini, Kamyar; Ilie, Mousa; Mirzazadeh, Mohammad; Baleanu, Dumitru; 56389
The main aim of the current article is considering a nonlinear time-fractional Cauchy reaction-diffusion equation with the Mittag-Leffler law and deriving its approximate analytical solution in a systematic way. More precisely, after reformulating the nonlinear time-fractional Cauchy reaction-diffusion equation with the Mittag-Leffler law, its approximate analytical solution is derived formally through the use of the homotopy analysis transform method (HATM) which is based on the homotopy method and the Laplace transform. The existence and uniqueness of the solution of the nonlinear time-fractional Cauchy reaction-diffusion equation with the Mittag-Leffler law are also studied by adopting the fixed-point theorem. In the end, by considering some two- and three-dimensional graphs, the influence of the order of time-fractional operator on the displacement is examined in detail.
Citation Count: Hosseini, Kamyar...et al. (20219. "An effective computational method to deal with a time-fractional nonlinear water wave equation in the Caputo sense", Mathematics and Computers in Simulation, Vol. 187, pp. 248-260.
An effective computational method to deal with a time-fractional nonlinear water wave equation in the Caputo sense
(2021) Hosseini, Kamyar; Ilie, Mousa; Mirzazadeh, Mohammad; Yusuf, Abdullahi; Sulaiman, Tukur Abdulkadi; Baleanu, Dumitru; Salahshour, Soheil; 56389
The authors' concern of the present paper is to conduct a systematic study on a time-fractional nonlinear water wave equation which is an evolutionary version of the Boussinesq system. The study goes on by adopting a new analytical method based on the Laplace transform and the homotopy analysis method to the governing model and obtaining its approximate solutions in the presence of the Caputo fractional derivative. To analyze the influence of the Caputo operator on the dynamical behavior of the approximate solutions, some graphical illustrations in two- and three-dimensions are formally presented. Furthermore, several numerical tables are given to support the performance of the new analytical method in handling the time-fractional nonlinear water wave equation. (C) 2021 International Association for Mathematics and Computers in Simulation (IMACS). Published by Elsevier B.V. All rights reserved.
Citation Count: İnç, Mustafa...et al. (2019). "N-wave and other solutions to the B-type Kadomtsev-Petviashvili equation", Thermal Science, Vol. 23, pp. S2027-S2035.
N-wave and other solutions to the B-type Kadomtsev-Petviashvili equation
(2019) İnç, Mustafa; Hosseini, Kamyar; Samavat, Majid; Mirzazadeh, Mohammad; Eslami, Mostafa; Moradi, Mojtaba; Baleanu, Dumitru; 56389
The present article studies a B-type Kadomtsev-Petviashvili equation with certain applications in the fluids. Stating with the Hirota's bilinear form and adopting reliable methodologies, a group of exact solutions such as the N-wave and other solutions to the B-type Kadomtsev-Petviashvili equation is formally derived. Some figures in two and three dimensions are given to illustrate the characteristics of the obtained solutions. The results of the current work actually help to complete the previous studies about the B-type Kadomtsev-Petviashvili equation.
Citation Count: Hosseini, Kamyar...et al. (2020). "Solitons and Jacobi Elliptic Function Solutions to the Complex Ginzburg–Landau Equation", Frontiers in Physics, Vol. 8.
Solitons and Jacobi Elliptic Function Solutions to the Complex Ginzburg–Landau Equation
(2020) Hosseini, Kamyar; Mirzazadeh, Mohammad; Osman, M.S.; Al Qurashi, Maysaa; Baleanu, Dumitru; 56389
The complex Ginzburg–Landau (CGL) equation which describes the soliton propagation in the presence of the detuning factor is firstly considered; then its solitons as well as Jacobi elliptic function solutions are obtained systematically using a modified Jacobi elliptic expansion method. In special cases, several dark and bright soliton solutions to the CGL equation are retrieved when the modulus of ellipticity approaches unity. The results presented in the current work can help to complete previous studies on the complex Ginzburg–Landau equation.
Citation Count: Hosseini, Kamyar...et.al. (2021). "The (2 + 1)-dimensional Heisenberg ferromagnetic spin chain equation: its solitons and Jacobi elliptic function solutions", The European Physical Journal Plus, Vol.136, No.2.
The (2 + 1)-dimensional Heisenberg ferromagnetic spin chain equation: its solitons and Jacobi elliptic function solutions
(2021) Hosseini, Kamyar; Salahshour, Soheil; Mirzazadeh, Mohammad; Ahmadian, Ali; Baleanu, Dumitru; Khoshrang, Arian; 56389
The search for exact solutions of nonlinear evolution models with different wave structures has achieved significant attention in recent decades. The present paper studies a nonlinear (2 + 1)-dimensional evolution model describing the propagation of nonlinear waves in Heisenberg ferromagnetic spin chain system. The intended aim is carried out by considering a specific transformation and adopting a modified version of the Jacobi elliptic expansion method. As a result, a number of solitons and Jacobi elliptic function solutions to the Heisenberg ferromagnetic spin chain equation are formally derived. Several three-dimensional plots are presented to demonstrate the dynamical features of the bright and dark soliton solutions.
Citation Count: Hosseini, Kamyar...et al. (2021). "The (2+1)-dimensional Heisenberg ferromagnetic spin chain equation: its solitons and Jacobi elliptic function solutions", European Physical Journal Plus, Vol. 136, No. 2.
The (2+1)-dimensional Heisenberg ferromagnetic spin chain equation: its solitons and Jacobi elliptic function solutions
(2021) Hosseini, Kamyar; Salahshour, Soheil; Mirzazadeh, Mohammad; Ahmadian, Ali; Baleanu, Dumitru; Khoshrang, Arian; 56389
The search for exact solutions of nonlinear evolution models with different wave structures has achieved significant attention in recent decades. The present paper studies a nonlinear (2+1)-dimensional evolution model describing the propagation of nonlinear waves in Heisenberg ferromagnetic spin chain system. The intended aim is carried out by considering a specific transformation and adopting a modified version of the Jacobi elliptic expansion method. As a result, a number of solitons and Jacobi elliptic function solutions to the Heisenberg ferromagnetic spin chain equation are formally derived. Several three-dimensional plots are presented to demonstrate the dynamical features of the bright and dark soliton solutions.
Citation Count: Baleanu, Dumitru...et al. (2021). "The (2+1)-dimensional hyperbolic nonlinear Schrodinger equation and its optical solitons", AIMS Mathematics, Vol. 6, No. 9, pp. 9568-9581.
The (2+1)-dimensional hyperbolic nonlinear Schrodinger equation and its optical solitons
(2021) Baleanu, Dumitru; Hosseini, Kamyar; Salahshour, Soheil; Sadri, Khadijeh; Mirzazadeh, Mohammad; Park, Choonkil; Ahmadian, Ali; 56389
A comprehensive study on the (2+1)-dimensional hyperbolic nonlinear Schrodinger (2D-HNLS) equation describing the propagation of electromagnetic fields in self-focusing and normally dispersive planar wave guides in optics is conducted in the current paper. To this end, after reducing the 2D-HNLS equation to a one-dimensional nonlinear ordinary differential (1D-NLOD) equation in the real regime using a traveling wave transformation, its optical solitons are formally obtained through a group of well-established methods such as the exponential and Kudryashov methods. Some graphical representations regarding optical solitons that are categorized as bright and dark solitons are considered to clarify the dynamics of the obtained solutions. It is noted that some of optical solitons retrieved in the current study are new and have been not retrieved previously.
Citation Count: Hosseini, Kamyar...et.al. (2022). "The Caputo-Fabrizio time-fractional Sharma-Tasso-Olver-Burgers equation and its valid approximations", Communications in Theoretical Physics, Vol.74, No.7.
The Caputo-Fabrizio time-fractional Sharma-Tasso-Olver-Burgers equation and its valid approximations
(2022) Hosseini, Kamyar; Ilie, Mousa; Mirzazadeh, Mohammad; Baleanu, Dumitru; Park, Choonkil; Salahshour, Soheil; 56389
Studying the dynamics of solitons in nonlinear time-fractional partial differential equations has received substantial attention, in the last decades. The main aim of the current investigation is to consider the time-fractional Sharma-Tasso-Olver-Burgers (STOB) equation in the Caputo-Fabrizio (CF) context and obtain its valid approximations through adopting a mixed approach composed of the homotopy analysis method (HAM) and the Laplace transform. The existence and uniqueness of the solution of the time-fractional STOB equation in the CF context are investigated by demonstrating the Lipschitz condition for φx,t;u as the kernel and giving some theorems. To illustrate the CF operator effect on the dynamics of the obtained solitons, several two- and three-dimensional plots are formally considered. It is shown that the mixed approach is capable of producing valid approximations to the time-fractional STOB equation in the CF context.