Related references
Note: Only part of the references are listed.
Article
Mathematics, Interdisciplinary Applications
Elsayed M. E. Zayed et al.
Summary: The objective of this paper is to study the cubic-quartic embedded solitons with second and third order nonlinear susceptibilities having multiplicative white noise in the Ito sense. The unified Riccati equation expansion method and the addendum Kudryashov's method are employed to accomplish this task. The straddled soliton, the combo bright-singular soliton, the bright soliton, the singular soliton solutions as long as periodic and rational solutions are obtained. The numerical schemes give a visual perspective to the solutions derived analytically.
CHAOS SOLITONS & FRACTALS
(2023)
Article
Mathematics, Interdisciplinary Applications
Salman A. AlQahtani et al.
Summary: The objective of this article is to investigate highly dispersive embedded solitons characterized by ?((2)) and ?((3)) non-linear susceptibilities, and incorporating multiplicative white noise in the Ito sense. To achieve this, we utilize both the new auxiliary equation method and an addendum to Kudryashov's method. The analysis conducted in this study results in solutions for bright solitons, singular solitons, and combo bright-singular solitons. Simulations of the bright soliton solutions are given. The system being studied and the outcomes outlined in the manuscript are innovative and original.
CHAOS SOLITONS & FRACTALS
(2023)
Article
Engineering, Electrical & Electronic
Salman A. A. AlQahtani et al.
Summary: This study establishes dispersive solitons of the Schrodinger-Hirota equation in polarization-preserving fibers. The Schrodinger-Hirota equation is examined using the P-6-model expansion method. As a result, a broad range of Jacobi-elliptic solutions, including dark solitons, bright solitons, combined dark-bright solitons, singular solitons, and periodic wave solutions, are generated.
OPTICAL AND QUANTUM ELECTRONICS
(2023)
Article
Physics, Multidisciplinary
Qin Zhou
Summary: The interaction between optical solitons plays a crucial role in studying the interaction between light and matter, as well as the development of all-optical devices and the design of integrated optical paths. This study investigates the interaction of optical solitons based on the nonlinear Schrodinger equation, aiming to improve communication quality and system integration. By deriving solutions to the equation, the interaction of two solitons is analyzed, and suggestions are proposed to weaken their interactions.
CHINESE PHYSICS LETTERS
(2022)
Article
Optics
Nikolay A. Kudryashov
Summary: This paper considers a new generalization of the nonlinear Schrodinger equation with triple refractive index and non-local nonlinearity, and presents a new form of optical solitons. An auxiliary nonlinear differential equation of the first order with a double nonlinearity is introduced to find exact solutions of the nonlinear partial differential equation. The results show the existence of new type optical solitons of the generalized Schrodinger equation expressed via implicit functions.
Article
Optics
Nikolay A. Kudryashov
Summary: This paper considers the complex Ginzburg-Landau equation with a polynomial law of nonlinearity with four powers. The Cauchy problem for this equation cannot be solved using the inverse scattering transform. However, the equation admits the translation groups in two independent variables and the general solution is sought using the traveling wave reduction method. A first integral of the nonlinear ordinary differential equation corresponding to the complex Ginzburg-Landau equation is found and reduced to a first-order nonlinear ordinary differential equation with the general solution expressed in terms of elliptic functions. The direct method allows for exact solutions without constraints on the parameters of the mathematiocal model. Partial cases of bright and dark optical solitons of the equation are given.
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
Optics
Nikolai A. Kudryashov et al.
Summary: This paper recovers dark and bright cubic-quartic optical solitons using the cubic-quintic-septicnonic nonlinear Schrodinger's equation, and then identifies the conserved quantities associated with the bright soliton using Gauss' hypergeometric functions.
Article
Optics
Lu Tang
Summary: This work mainly focuses on the dynamical behavior and optical solitons for the dual-mode nonlinear Schrodinger equation with Kerr law nonlinearity. The dark soliton solutions and singular soliton solutions are analytically constructed using the bifurcation method of dynamical system. Additionally, other soliton solutions, including rational function solutions and Jacobian elliptic solutions, are derived using the complete discriminant method and symbolic computation. The obtained solutions may improve or complement previous results, and inspire exploration of new complex physical phenomena in this system.
Article
Mathematics
Elsayed M. E. Zayed et al.
Summary: The current article investigates optical soliton solutions for the dimensionless form of the stochastic resonant nonlinear Schrodinger equation with both spatio-temporal dispersion and inter-modal dispersion, along with multiplicative noise in the ito sense. Seven laws of nonlinearities, including the Kerr law, power law, parabolic law, dual-power law, quadratic-cubic law, polynomial law, and triple-power law, are discussed. The new auxiliary equation method is applied to secure bright, dark, and singular soliton solutions for the model.
Article
Mathematics, Applied
Elsayed M. E. Zayed et al.
Summary: This paper employs three integration algorithms to extract optical soliton solutions for the generalized Kudryashov equation, finding various types of solitons.
MATHEMATICAL METHODS IN THE APPLIED SCIENCES
(2021)
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
Engineering, Electrical & Electronic
Elsayed M. E. Zayed et al.
Summary: This paper investigates optical solitons in Bragg gratings fibers using NLSE with cubic-quartic dispersive reflectivity and parabolic non-local combo law of refractive index. The extended auxiliary equation method and an addendum to Kudryashov's method are introduced to determine the existence criteria for such solitons.
OPTICAL AND QUANTUM ELECTRONICS
(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
Physics, Multidisciplinary
Khalid K. Ali et al.
Article
Chemistry, Multidisciplinary
Khaled A. Gepreel
APPLIED SCIENCES-BASEL
(2020)
Article
Physics, Multidisciplinary
Hamdy M. Ahmed et al.
Article
Optics
Salam Khan
Article
Physics, Multidisciplinary
Houria Triki et al.
WAVES IN RANDOM AND COMPLEX MEDIA
(2017)
