Browsing by Author "Mirzazadeh, M."

Now showing 1 - 15 of 15

Citation - WoS: 8
Citation - Scopus: 12
A detailed study on a new (2+1)-dimensional mKdV equation involving the Caputo-Fabrizio time-fractional derivative
(Springer, 2020) Hosseini, K.; Ilie, M.; Mirzazadeh, M.; Baleanu, D.; 56389; Matematik
The present article aims to present a comprehensive study on a nonlinear time-fractional model involving the Caputo-Fabrizio (CF) derivative. More explicitly, a new (2+1)-dimensional mKdV (2D-mKdV) equation involving the Caputo-Fabrizio time-fractional derivative is considered and an analytic approximation for it is retrieved through a systematic technique, called the homotopy analysis transform (HAT) method. Furthermore, after proving the Lipschitz condition for the kernel psi (x,y,t;u), the fixed-point theorem is formally utilized to demonstrate the existence and uniqueness of the solution of the new 2D-mKdV equation involving the CF time-fractional derivative. A detailed study finally is carried out to examine the effect of the Caputo-Fabrizio operator on the dynamics of the obtained analytic approximation.
Citation - Scopus: 10
A New (4 + 1)-Dimensional Burgers Equation: Its Bäcklund Transformation and Real and Complex -Kink Solitons
(Springer, 2022) Hosseini, K.; Samavat, M.; Mirzazadeh, M.; Salahshour, S.; Baleanu, D.; 56389; Matematik
Studying the dynamics of solitons in nonlinear evolution equations (NLEEs) has gained considerable interest in the last decades. Accordingly, the search for soliton solutions of NLEEs 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 dispersive waves in nonlinear sciences. Based on the truncated Painlevé expansion, the Bäcklund transformation of the n4D-BE is firstly extracted, then, its real and complex N-kink solitons are derived using the simplified Hirota method. Furthermore, several ansatz methods are formally adopted to obtain a group of other single-kink soliton solutions of the n4D-BE. © 2022, The Author(s), under exclusive licence to Springer Nature India Private Limited.
Citation - WoS: 16
Citation - Scopus: 16
A new generalized KdV equation: Its lump-type, complexiton and soliton solutions
(World Scientific Publ Co Pte Ltd, 2022) Hosseini, K.; Salahshour, S.; Baleanu, D.; Mirzazadeh, M.; Dehingia, K.; 56389; Matematik
A new generalized KdV equation, describing the motions of long waves in shallow water under the gravity field, is considered in this paper. By adopting a series of well-organized methods, the Backlund transformation, the bilinear form and diverse wave structures of the governing model are formally extracted. The exact solutions listed in this paper are categorized as lump-type, complexiton, and soliton solutions. To exhibit the physical mechanism of the obtained solutions, several graphical illustrations are given for particular choices of the involved parameters. As a direct consequence, diverse wave structures given in this paper enrich the studies on the KdV-type equations.
Citation - Scopus: 2
Bäcklund Transformation, Complexiton, and Solitons of a (4 + 1)-dimensional Nonlinear Evolutionary Equation
(Springer, 2022) Hosseini, K.; Salahshour, S.; Baleanu, D.; Mirzazadeh, M.; 56389; Matematik
The main purpose of the current paper is to establish a (4 + 1)-dimensional nonlinear evolutionary (4D-NLE) equation and derive its Bäcklund transformation, complexiton, and solitons. To this end, the Bäcklund transformation of the 4D-NLE equation is first constructed by applying the truncated Painlevé expansion. The simplified Hirota’s method is then employed to acquire the solitons of the governing model. In the end, the complexiton of the 4D-NLE equation is retrieved using the Zhou–Ma method. As the completion of studies, several graphical representations are considered for different parameter values to show the dynamics of complexiton and solitons. © 2022, The Author(s), under exclusive licence to Springer Nature India Private Limited.
Citation - WoS: 116
Citation - Scopus: 126
Double-wave solutions and Lie symmetry analysis to the (2+1)-dimensional coupled Burgers equations
(Elsevier, 2020) Osman, M. S.; Baleanu, D.; Adem, A. R.; Hosseini, K.; Mirzazadeh, M.; Eslami, M.; 56389; Matematik
This paper investigates the (2 + 1)-dimensional coupled Burgers equations (CBEs) which is an important nonlinear physical model. In this respect, by making use of the generalized unified method (GUM), a series of double-wave solutions of the (2 + 1)-dimensional coupled Burgers equations are derived. The Lie symmetry technique (LST) is also utilized for the symmetry reductions of the (2 + 1)-dimensional coupled Burgers equations and extracting a non-traveling wave solution. Through some figures, we discussed the wave structures of the double-wave solutions of the CBEs for different values of parameters in these solutions.
Citation - Scopus: 12
Multi-complexiton and positive multi-complexiton structures to a generalized B-type Kadomtsev−Petviashvili equation
(Shanghai Jiaotong University, 2022) Hosseini, K.; Baleanu, D.; Rezapour, S.; Salahshour, S.; Mirzazadeh, M.; Samavat, M.; 56389; Matematik
Recently, Zhang et al. (International Journal of Modern Physics B 30 (2016) 1640029) constructed N-wave solutions of a generalized B-type Kadomtsev−Petviashvili (gbKP) equation using the linear superposition method. The authors’ aim of the present paper is to derive multi-complexiton and positive multi-complexiton structures of the gbKP equation through considering N-wave solutions and applying specific systematic methods. To investigate the dynamical characteristics of positive multi-complexiton structures, particularly single and double positive complexitons, several two and three-dimensional simulations are formally considered. The results of the current research enrich the studies regarding the gbKP equation. © 2022
Citation - WoS: 30
Citation - Scopus: 36
Multiwave, multicomplexiton, and positive multicomplexiton solutions to a (3 + 1)-dimensional generalized breaking soliton equation
(Elsevier, 2020) Hosseini, K.; Seadawy, Aly R.; Mirzazadeh, M.; Eslami, M.; Radmehr, S.; Baleanu, Dumitru; 56389; Matematik
There are a lot of physical phenomena which their mathematical models are decided by nonlinear evolution (NLE) equations. Our concern in the present work is to study a special type of NLE equations called the (3 + 1)-dimensional generalized breaking soliton (3D-GBS) equation. To this end, the linear superposition (LS) method along with a series of specific techniques are utilized and as an achievement, multiwave, multicomplexiton, and positive multicomplexiton solutions to the 3D-GBS equation are formally constructed. The study confirms the efficiency of the methods in handling a wide variety of nonlinear evolution equations. (C) 2020 The Authors. Published by Elsevier B.V. on behalf of Faculty of Engineering, Alexandria University.
Citation - WoS: 46
Citation - Scopus: 51
Optical solitons of a high-order nonlinear Schrödinger equation involving nonlinear dispersions and Kerr effect
(Springer, 2022) Hosseini, K.; Mirzazadeh, M.; Baleanu, D.; Salahshour, S.; Akinyemi, L.; 56389; Matematik
The main aim of this paper is to conduct a detailed study on a high-order nonlinear Schrodinger (HONLS) equation involving nonlinear dispersions and the Kerr effect. More precisely, after reducing the governing model describing ultra-short pulses in optical fibers in a one-dimensional domain, its optical solitons including the bright and dark solitons are derived through the modified Kudryashov (MK) method. The dynamical behavior of the bright and dark solitons is formally investigated for different sets of the involved parameters. It is shown that increasing and decreasing nonlinear dispersions lead to significant changes in the amplitude of the bright and dark solitons.
Citation - WoS: 11
Citation - Scopus: 12
Optical solitons to the Ginzburg–Landau equation including the parabolic nonlinearity
(Springer, 2022) Hosseini, K.; Mirzazadeh, M.; Akinyemi, L.; Baleanu, D.; Salahshour, S.; 56389; Matematik
The major goal of the present paper is to construct optical solitons of the Ginzburg-Landau equation including the parabolic nonlinearity. Such an ultimate goal is formally achieved with the aid of symbolic computation, a complex transformation, and Kudryashov and exponential methods. Several numerical simulations are given to explore the influence of the coefficients of nonlinear terms on the dynamical features of the obtained optical solitons. To the best of the authors' knowledge, the results reported in the current study, classified as bright and kink solitons, have a significant role in completing studies on the Ginzburg-Landau equation including the parabolic nonlinearity.
Citation - WoS: 11
Citation - Scopus: 11
Soliton structures of a nonlinear Schrödinger equation involving the parabolic law
(Springer, 2021) Salahshour, S.; Hosseini, K.; Mirzazadeh, M.; Baleanu, D.; 56389; Matematik
The search for soliton structures plays a pivotal role in many scientific disciplines particularly in nonlinear optics. The main concern of the present paper is to explore the dynamics of soliton structures in a nonlinear Schrodinger (NLS) equation with the parabolic law. In this respect, the reduced form of the NLS equation is firstly extracted; then, its soliton structures are derived in the presence of spatio-temporal dispersions using the Kudryashov method. As the completion of studies, the impact of increasing and decreasing the coefficients of the parabolic law on the dynamics of soliton structures is formally addressed through representing several two- and three-dimensional figures.
Citation - WoS: 26
Citation - Scopus: 33
Specific wave structures of a fifth-order nonlinear water wave equation
(Elsevier, 2022) Hosseini, K.; Mirzazadeh, M.; Salahshour, S.; Baleanu, D.; Zafar, A.; 56389; Matematik
Investigated in the present paper is a fifth-order nonlinear evolution (FONLE) equation, known as a non-linear water wave (NLWW) equation, with applications in the applied sciences. More precisely, a travel-ing wave hypothesis is firstly applied that reduces the FONLE equation to a 1D domain. The Kudryashov methods (KMs) are then adopted as leading techniques to construct specific wave structures of the gov-erning model which are classified as W-shaped and other solitons. In the end, the effect of changing the coefficients of nonlinear terms on the dynamical features of W-shaped and other solitons is investigated in detail for diverse groups of the involved parameters.(c) 2021 Shanghai Jiaotong University. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license ( http://creativecommons.org/licenses/by-nc-nd/4.0/ )
Citation - WoS: 29
Citation - Scopus: 39
The generalized complex Ginzburg–Landau model and its dark and bright soliton solutions
(Springer Heidelberg, 2021) Hosseini, K.; Mirzazadeh, M.; Baleanu, D.; Raza, N.; Park, C.; Ahmadian, A.; Salahshour, S.; 56389; Matematik
In the present work, the generalized complex Ginzburg-Landau (GCGL) model is considered and its 1-soliton solutions involving different wave structures are retrieved through a series of newly well-organized methods. More exactly, after considering the GCGL model, its 1-soliton solutions are obtained using the exponential and Kudryashov methods in the presence of perturbation effects. As a case study, the effect of various parameter regimes on the dynamics of the dark and bright soliton solutions is analyzed in three- and two-dimensional postures. The validity of all the exact solutions presented in this study has been examined successfully through the use of the symbolic computation system.
Citation - WoS: 23
Citation - Scopus: 22
The generalized Sasa–Satsuma equation and its optical solitons
(Springer, 2022) Hosseini, K.; Sadri, K.; Salahshour, S.; Baleanu, D.; Mirzazadeh, M.; Inc, Mustafa; 56389; Matematik
The principal goal of the presented paper is to investigate the dynamics of optical solitons for the generalized Sasa-Satsuma (GSS) equation describing the propagation of the femtosecond pulses in the systems of optical fiber transmission. More precisely, the governing model, which is a generalized version of the classical Sasa-Satsuma equation, is firstly reduced in a one-dimensional real regime through a specific transformation; then, its bright and dark optical solitons are established using the modified Kudryashov (MK) method. The changes in the amplitude of the bright and dark solitons are analyzed as a case study for various classes of free parameters. Considerable changes are observed in the optical solitons amplitude from the results presented in the current study.
Citation - WoS: 22
Citation - Scopus: 22
The geophysical KdV equation: its solitons, complexiton, and conservation laws
(Springer Heidelberg, 2022) Hosseini, K.; Akbulut, A.; Baleanu, D.; Salahshour, S.; Mirzazadeh, M.; Akinyemi, L.; 56389; Matematik
The main goal of the current paper is to analyze the impact of the Coriolis parameter on nonlinear waves by studying the geophysical KdV equation. More precisely, specific transformations are first adopted to derive one-dimensional and operator forms of the governing model. Solitons and complexiton of the geophysical KdV equation are then retrieved with the help of several well-established approaches such as the Kudryashov and Hirota methods. In the end, the new conservation theorem given by Ibragimov is formally employed to extract conservation laws of the governing model. It is shown that by increasing the Coriolis parameter, based on the selected parameter regimes, less time is needed for tending the free surface elevation to zero.
Citation - Scopus: 10
The Korteweg-de Vries–Caudrey–Dodd–Gibbon dynamical model: Its conservation laws, solitons, and complexiton
(Shanghai Jiaotong University, 2022) Hosseini, K.; Akbulut, A.; Baleanu, D.; Salahshour, S.; Mirzazadeh, M.; Dehingia, K.; 56389; Matematik
The main purpose of the present paper is to conduct a detailed and thorough study on the Korteweg-de Vries–Caudrey–Dodd–Gibbon (KdV-CDG) dynamical model. More precisely, after considering the integrable KdV-CDG dynamical model describing certain properties of ocean dynamics, its conservation laws, solitons, and complexiton are respectively derived using the Ibragimov, Kudryashov, and Hirota methods. Several numerical simulations in two and three-dimensional postures are formally given to analyze the effect of nonlinear parameters. It is shown that nonlinear parameters play a key role in the dynamical properties of soliton and complexiton solutions. © 2022