Browsing by Author "Hosseini, K."

Now showing 1 - 20 of 24

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; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
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: 9
Citation - Scopus: 14
A Detailed Study on a New (2+1)-Dimensional Mkdv Equation Involving the Caputo-Fabrizio Time-Fractional Derivative
(Springer, 2020) Mirzazadeh, M.; Baleanu, D.; Hosseini, K.; Ilie, M.; 56389; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
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: 11
A Detailed Study on a Tumor Model With Delayed Growth of Pro-Tumor Macrophages
(Springer, 2022) Dehingia, K.; Hosseini, K.; Salahshour, S.; Baleanu, D.; 56389; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
This paper investigates a tumor-macrophages interaction model with a discrete-time delay in the growth of pro-tumor M2 macrophages. The steady-state analysis of the governing model is performed around the tumor dominant steady-state and the interior steady-state. It is found that the tumor dominant steady-state is locally asymptotically stable under certain conditions, and the stability of the interior steady-state is affected by the discrete-time delay; as a result, the unstable system experiences a Hopf bifurcation and gets stabilized. Furthermore, the transversality conditions for the existence of Hopf bifurcations are derived. Several graphical representations in two and three-dimensional postures are given to examine the validity of the results provided in the current study. © 2022, The Author(s), under exclusive licence to Springer Nature India Private Limited.
Citation - WoS: 117
Citation - Scopus: 127
Double-Wave Solutions and Lie Symmetry Analysis To the (2+1)-Dimensional Coupled Burgers Equations
(Elsevier, 2020) Eslami, M.; Osman, M. S.; Baleanu, D.; Adem, A. R.; Hosseini, K.; Mirzazadeh, M.; 56389; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
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 - WoS: 28
Citation - Scopus: 31
Effect of Ion and Negative Ion Temperatures on Kdv and Mkdv Solitons in a Multicomponent Plasma
(Springer, 2023) Madhukalya, B.; Das, R.; Hosseini, K.; Baleanu, D.; Hincal, E.; 56389; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
The formation of ion-acoustic solitons (IASs) in an unmagnetized plasma with negative ions has been investigated through the KdV equation in both the situations Q'( = m(j)=m(i)= negative to positive ion mass ratio) less and greater than one and the mKdV equation only for Q' > 1. The existence of both KdV and mKdV solitons has been established for alpha (= ion to electron temperature ratio) > beta (= negative ion to electron temperature ratio) and alpha < beta, which is the new outcome of the current investi-gation. Furthermore, the existence of both compres-sive and rarefactive solitons for Q' > 1 and Q'< 1 has been demonstrated. A dispersion capable action. and
Citation - WoS: 3
Citation - Scopus: 4
Further Studies on Ordinary Differential Equations Involving the M-Fractional Derivative
(Amer inst Mathematical Sciences-aims, 2022) Khoshkenar, A.; Ilie, M.; Hosseini, K.; Baleanu, D.; Salahshour, S.; Park, C.; Lee, J. R.; 56389; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
In the current paper, the power series based on the M-fractional derivative is formally introduced. More peciesely, the Taylor and Maclaurin expansions are generalized for fractional-order differentiable functions in accordance with the M-fractional derivative. Some new definitions, theorems, and corollaries regarding the power series in the M sense are presented and formally proved. Several ordinary differential equations (ODEs) involving the M-fractional derivative are solved to examine the validity of the results presented in the current study.
Citation - WoS: 31
Citation - Scopus: 40
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; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
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: 23
The Generalized Sasa-Satsuma Equation and Its Optical Solitons
(Springer, 2022) Hosseini, K.; Sadri, K.; Salahshour, S.; Baleanu, D.; Mirzazadeh, M.; Inc, Mustafa; 56389; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
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: 23
Citation - Scopus: 23
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; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
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: 4
Ion-Acoustic Solitons in Magnetized Plasma Under Weak Relativistic Effects on the Electrons
(Springer, 2023) Madhukalya, B.; Das, R.; Hosseini, K.; Baleanu, D.; Salahshour, S.; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
Investigating ion-acoustic disturbances in a magnetized plasma, consisting of relativistic electrons and non-thermal ions, entails a comprehensive study into the nonlinear wave structure. By condensing the fundamental set of fluid equations for the flow variables, a singular equation known as the Sagdeev potential equation is derived using the pseudopotential approach. In this investigation of the magnetized relativistic plasma, we have observed only dip (rarefactive) (N< 1) soliton under both subsonic (M< 1) and supersonic (M> 1) conditions. The occurrence of the soliton depends on the wave velocities in different propagation directions. The magnitude of amplitudes of the relativistic solitons is higher for higher Mach number (M> 1) irrespective of the wave’s propagation direction. Furthermore, the magnitude of amplitudes of the solitary wave is seen to increase near the direction of the magnetic field. © 2023, The Author(s), under exclusive licence to Springer Nature India Private Limited.
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; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
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
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; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
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: 31
Citation - Scopus: 38
Multiwave, Multicomplexiton, and Positive Multicomplexiton Solutions To a (3
(Elsevier, 2020) Seadawy, Aly R.; Mirzazadeh, M.; Eslami, M.; Radmehr, S.; Baleanu, Dumitru; Hosseini, K.; 56389; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
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 - Scopus: 10
A New (4 + 1)-Dimensional Burgers Equation: Its Bäcklund Transformation and Real and Complex N -Kink Solitons
(Springer, 2022) Samavat, M.; Mirzazadeh, M.; Salahshour, S.; Baleanu, D.; Hosseini, K.; 56389; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
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: 17
Citation - Scopus: 17
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; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
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 - WoS: 39
Citation - Scopus: 42
Non-Singular Multi-Complexiton Wave To a Generalized Kdv Equation
(Springer, 2023) Hosseini, K.; Hincal, E.; Baleanu, D.; Obi, O. A.; Salahshour, S.; 56389; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
The major goal of the current paper is to conduct a detailed study on a generalized KdV equation (gKdVE) and its non-singular multi-complexiton wave. More precisely, first the multi-shock wave of the governing model is retrieved using the principle of linear superposition. Based on the multi-shock wave and the techniques adopted by Zhou and Manukure, the non-singular multi-complexiton wave to the gKdVE is then constructed with the help of symbolic computations. The dynamical properties of single and double shock waves as well as non-singular single and double complexiton waves are analyzed by representing a group of 3D-plots. The achievements of the present paper take an important step in completing the research on the generalized KdV equation.
Citation - WoS: 51
Citation - Scopus: 54
Optical Solitons of a High-Order Nonlinear Schrodinger Equation Involving Nonlinear Dispersions and Kerr Effect
(Springer, 2022) Baleanu, D.; Salahshour, S.; Akinyemi, L.; Hosseini, K.; Mirzazadeh, M.; 56389; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
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: 12
Citation - Scopus: 13
Optical Solitons To the Ginzburg-Landau Equation Including the Parabolic Nonlinearity
(Springer, 2022) Hosseini, K.; Mirzazadeh, M.; Akinyemi, L.; Baleanu, D.; Salahshour, S.; 56389; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
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: 21
Citation - Scopus: 26
Periodic and Solitary Waves of the Nonlinear Konno-Oono Model: Generalized Methods
(Springer, 2023) Hosseini, K.; Sadri, K.; Hincal, E.; Abbasi, A.; Baleanu, D.; Salahshour, S.; 56389; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
There has been considerable academic interest in the study of nonlinear dynamical models and their exact traveling waves over the past few years. The main aim of the present paper is to consider a nonlinear dynamical model known as the nonlinear Konno-Oono model and derive its exact traveling waves. Specifically, after applying a universal transformation, periodic and solitary waves of the governing model with applications in the electromagnetic field are derived using generalized methods. Through the consideration of two- and three-dimensional simulations, several case studies are considered to represent the dynamical behavior of soliton solutions.
Citation - WoS: 24
The Sharma-Tasso Equation: Its Conservation Laws and Kink Solitons
(Iop Publishing Ltd, 2022) Hosseini, K.; Akbulut, A.; Baleanu, D.; Salahshour, S.; 56389; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
The present paper deals with the Sharma-Tasso-Olver-Burgers equation (STOBE) and its conservation laws and kink solitons. More precisely, the formal Lagrangian, Lie symmetries, and adjoint equations of the STOBE are firstly constructed to retrieve its conservation laws. Kink solitons of the STOBE are then extracted through adopting a series of newly well-designed approaches such as Kudryashov and exponential methods. Diverse graphs in 2 and 3D postures are formally portrayed to reveal the dynamical features of kink solitons. According to the authors' knowledge, the outcomes of the current investigation are new and have been listed for the first time.