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Article
Mathematics, Interdisciplinary Applications
Ahmed H. Arnous et al.
Summary: This paper implements the enhanced Kudryashov's method to address the solitons of the cubic-quartic complex Ginzburg-Landau equation. Different forms of self-phase modulation structures are studied, and the existence criteria for bright and singular solitons are indicated.
CHAOS SOLITONS & FRACTALS
(2022)
Article
Optics
Ahmed H. Arnous
Summary: This study introduces a new simple integration technique to extract optical solitons for cubic quartic Bragg-gratings with anti-cubic nonlinear form, including bright, dark, and singular soliton solutions, as well as bright-dark hybrid soliton solutions. The results demonstrate that the method is simple and effective for seeking exact solutions and extracting optical solitons, with appropriate constraints to guarantee their existence.
Article
Physics, Multidisciplinary
Ahmed H. Arnous et al.
Summary: This paper utilizes an enhanced version of Kudryashov's scheme to investigate optical soliton solutions in fiber Bragg gratings with five different nonlinear forms. The analysis incorporates the effect of cubic-quartic dispersive reflectivity, resulting in a full spectrum of solitons for various cases.
Article
Physics, Applied
Neslihan Ozdemir et al.
Summary: This research paper scrutinizes novel traveling wave solutions and other solutions with conformable, M-truncated, and beta fractional derivatives for the nonlinear fractional Hirota-Maccari system. The Riccati-Bernoulli sub-ODE technique is implemented to acquire the analytical solutions. The paper provides mathematical properties of different kinds of fractional derivatives and presents a comparative approach between the solutions using fractional derivatives.
MODERN PHYSICS LETTERS B
(2022)
Article
Optics
Nikolay A. Kudryashov
Summary: The generalized nonlinear Schrodinger equation with nonlinear chromatic dispersion and polynomial powers with arbitrary refractive index is analyzed. The first integral of the nonlinear ordinary differential equation corresponding to the stationary solution of the equation is derived. Analytical solutions for bright and dark stationary optical solitons described by the generalized mathematical model are obtained using variable transformations.
Article
Physics, Multidisciplinary
Nikolay A. Kudryashov
Summary: The generalized nonlinear Schrodinger equation for optical solitons in a saturable medium is studied using transformation variables to find solitary wave solutions. Analytical solutions for bright and dark solitons in a saturable medium are demonstrated.
Article
Physics, Applied
Handenur Esen et al.
Summary: This paper presents the analytical soliton solutions of the higher-order nonlinear Schrodinger equation (NLSE) with third and fourth-order dispersion and cubic-quintic nonlinearity terms. Two analytical methods, Kudryashov's method and the unified Riccati equation expansion method, are used to obtain the solutions. The physical behavior of the solutions is illustrated through 3D, 2D, and contour graphs and the effects of different coefficients on soliton dynamics are analyzed.
JOURNAL OF APPLIED PHYSICS
(2022)
Article
Engineering, Electrical & Electronic
Kalim U. Tariq et al.
Summary: This study investigates the Lakshmanan-Porsezian-Daniel model, which is a generalization of the non-linear Schrodinger model, to describe the dynamic behavior of optical solitons. The extended modified auxiliary equation mapping method is used to obtain new exact solitary wave solutions for complex models with different nonlinearities.
OPTICAL AND QUANTUM ELECTRONICS
(2022)
Article
Optics
Nikolay A. Kudryashov
Summary: This paper considers new generalized Schrodinger equations with polynomial nonlinearities. The inverse scattering transform cannot solve the Cauchy problem for these equations, hence, traveling wave solutions are sought for optical solitons. By using transformations of dependent and independent variables, solutions for nonlinear ordinary differential equations are found. These new auxiliary equations allow for the search for optical solitons of other generalized Schrodinger equations.
Article
Optics
Muslum Ozisik et al.
Summary: The main objective of this paper is to investigate soliton solutions of a nonlinear Schrodinger equation with sextic power-law nonlinearity. Two efficient analytical methods are introduced to solve the equation, and the results show that these methods can successfully obtain solutions of the equation and provide physical illustrations through graphs.
Article
Optics
Muslum Ozisik et al.
Summary: This manuscript investigates the optical soliton solution of the Manakov model using the auxiliary equation technique. By obtaining the nonlinear ordinary differential equation form and solving the linear algebraic system, the unknown parameters are obtained. The findings show that the effective auxiliary equation method can successfully obtain various types of soliton pulse solutions.
Article
Engineering, Electrical & Electronic
Muslum Ozisik et al.
Summary: In this paper, the perturbed Chen-Lee-Liu equation describing pulse propagation in optical fibers under the effects of inter-modal dispersion, self-steepening, and nonlinear dispersion terms was investigated. Using the enhanced modified extended tanh expansion method, various types of solitons were obtained, and the influence of coefficients of inter-modal dispersion, self-steepening, and nonlinear dispersion terms on soliton dynamics was examined.
OPTICAL AND QUANTUM ELECTRONICS
(2022)
Article
Optics
Selvi Altun et al.
Summary: This study examines the optical soliton solutions of the nonlinear Schrodinger form of the (2+1)-Biswas-Milovic equation with Kerr, power, and parabolic law nonlinearity. The new Kudryashov method is used to derive soliton solutions, and it is found that these solutions have basic soliton shapes. This investigation of the (2+1)-Biswas-Milovic equation with Kerr, power, and parabolic law nonlinearity is presented for the first time in this manuscript.
Article
Optics
Aydin Secer
Summary: This study examined the stochastic optical soliton solutions of the NLSE with Kerr law nonlinearity by multiplicative noise in Ito sense. The distortion of soliton solutions under different noise effects was clearly demonstrated and simulated.
Article
Optics
Ming-Yue Wang
Summary: In this paper, the perturbed nonlinear Schrodinger equation with dispersion terms of all orders and containing Kudryashov's sextic power law of self phase modulation is studied. Abundant exact solutions are obtained by combining the complete discriminant system for polynomial method with the trial equation method. The results of this paper provide a possibility for the analysis of complex optical phenomena.
Article
Optics
Muslum Ozisik et al.
Summary: In this study, we conducted a detailed research on Kudryashov methods and provided appropriate algorithms for each method. By applying these methods to a specific equation, we verified their effectiveness. The results showed that these methods can be widely and effectively used in solving nonlinear evolution problems as well as highly dispersive and higher order nonlinear partial differential equations. Additionally, we presented some new approaches and addendums in this field and solved the (2+1)-dimensional Zoomeron equation for the first time using these methods.
Article
Mathematics
Nikolay A. Kudryashov
Summary: This paper considers the family of generalized Schrodinger equations with unrestricted order Kerr nonlinearity. The solutions are found using traveling wave reductions and the Painleve test is applied to determine arbitrary constants in the general solution. It is shown that the equation does not pass the Painleve test but has two arbitrary constants, allowing for the search of solitary wave solutions. The main result of this paper is the theorem of existence of optical solitons for equations of unrestricted order, which is proved by direct calculation. Detailed optical solitons for twelfth order partial differential equations are provided.
Article
Optics
Ahmed H. Arnous et al.
Summary: This paper investigates soliton solutions to Kudryashov's equation using an improved approach, presenting bright, dark, and singular optical soliton solutions. The conserved quantities are also demonstrated.
Article
Optics
Abdul-Majid Wazwaz
Summary: This study addresses soliton propagation in a sixth-order nonlinear Schrodinger equation with fourth-order and sixth-order dispersive terms influenced by cubic-quintic-septic nonlinearities. Bright and dark optical soliton solutions are formally derived, with constraints on parameters for determining these solutions. Other ansatze are employed to determine additional singular and periodic solutions. The findings could enhance understanding of wave dynamics in cubic-quintic-septic nonlinear materials such as chalcogenide glass.
Article
Optics
Ming-Yue Wang
Summary: This paper demonstrates how to obtain analytical solutions of the perturbed nonlinear Schrodinger equation in the presence of time-and space-dependent dissipation (or gain) and nonlinear dispersion with Kerr law by complete discriminant system for polynomial method. The analytical solutions discussed include solitary wave solutions, Jacobian elliptic function solutions, triangular function solutions and rational solutions, and their effects on the propagations of optical pulse in dissipation (or gain) optical fibers are analyzed.
Article
Optics
Ahmed H. Arnous
Summary: In this study, an enhanced Kudryashov's algorithm is introduced to extract optical soliton solutions for the Biswas-Milovic equation in a magneto-optic waveguide coupled system with Kudryashov's law of refractive index. The obtained solitons, including bright, dark, and singular soliton solutions, appear with appropriate constraints to ensure their existence.
Article
Physics, Multidisciplinary
Mohammad Taghi Darvishi et al.
Summary: In this article, we introduce a family of nonlinear Schrodinger-type models with space-time fractional evolution using a conformable fractional derivative. The modified Kudryashov method is applied in the context of fractional complex transformation to seek optical soliton solutions for these equations. This method has been shown to be efficient and consistent in solving nonlinear space-time fractional differential equations.
Article
Mathematics, Interdisciplinary Applications
M. T. Darvishi et al.
Summary: This paper investigates space-time conformable fractional nonlinear (1+1)-dimensional Schrodinger-type models and presents traveling wave solutions using the sine-Gordon expansion approach. The paper uses the sine-Gordon expansion method to obtain exact solutions for three types of space-time conformable fractional nonlinear Schrodinger-type equations, some of which are new.
CHAOS SOLITONS & FRACTALS
(2021)
Article
Physics, Applied
Handenur Esen et al.
Summary: This paper discusses the edge states of the fractional quantum Hall effect defined by two nonlinear Schrodinger equations, and reports their solutions using a specific method. It demonstrates the generation of singular periodic waves, dark and singular optical soliton solutions, and showcases the importance of the presented equations in the real world through 3D and 2D graphs created with the MAPLE software.
MODERN PHYSICS LETTERS B
(2021)
Article
Materials Science, Multidisciplinary
Weitian Yu et al.
Summary: This paper studies the coupled Manakov equations with variable coefficients governing the transmission of orthogonally polarized pulses in two mode optical fibers using the Hirota method. A variety of soliton solutions are obtained and the dynamics of double-hump solitons in different modes are analyzed. The methods to regulate the phase shift, amplification, collision intensity, and splitting of double-hump solitons are investigated, aiming to improve the capacity of optical fiber communication systems and reduce bit error rates.
RESULTS IN PHYSICS
(2021)
Article
Optics
Nikolay A. Kudryashov
Article
Optics
Nikolay A. Kudryashov
Article
Mathematics, Interdisciplinary Applications
Russell W. Kohl et al.
CHAOS SOLITONS & FRACTALS
(2020)
Article
Materials Science, Multidisciplinary
Tukur Abdulkadir Sulaiman et al.
RESULTS IN PHYSICS
(2020)
Article
Mathematics, Interdisciplinary Applications
Nikolay A. Kudryashov
CHAOS SOLITONS & FRACTALS
(2020)
Article
Mathematics, Applied
Nikolay A. Kudryashov
REGULAR & CHAOTIC DYNAMICS
(2020)
Article
Optics
Russell W. Kohl et al.
Article
Engineering, Mechanical
Ahmed H. Arnous et al.
NONLINEAR DYNAMICS
(2017)
Article
Optics
Ahmed H. Arnous et al.
Article
Physics, Multidisciplinary
Jalil Manafian et al.
EUROPEAN PHYSICAL JOURNAL PLUS
(2015)
