Related references
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Article
Optics
Mehmet Ekici
Summary: This paper investigates the recovery of stationary optical solitons using Kudryashov's recently proposed nonlinear refractive index structure with quintuple power laws. The extended Jacobi's elliptic function expansion is employed as the integration algorithm, considering both linear and generalized formats of the temporal evolution term.
JOURNAL OF NONLINEAR OPTICAL PHYSICS & MATERIALS
(2023)
Article
Engineering, Mechanical
K. Hosseini et al.
Summary: 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. The multi-shock wave of the governing model is retrieved using the principle of linear superposition, and the non-singular multi-complexiton wave to the gKdVE is constructed with the help of symbolic computations. The dynamical properties of shock waves and complexiton waves are analyzed through 3D-plots, providing important progress in the research on the generalized KdV equation.
NONLINEAR DYNAMICS
(2023)
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Engineering, Mechanical
B. Madhukalya et al.
Summary: The formation of ion-acoustic solitons in an unmagnetized plasma with negative ions was investigated using the KdV equation. It was found that both KdV and mKdV solitons exist when the ion to electron temperature ratio is greater than the negative ion to electron temperature ratio. Additionally, compressive and rarefactive solitons were demonstrated for both Q' greater than 1 and Q' less than 1.
NONLINEAR DYNAMICS
(2023)
Article
Optics
K. Hosseini et al.
Summary: The main aim of this paper is to analyze the nonlinear effects on the dynamics of soliton waves in a nonlinear Schrödinger equation (NLSE) with the inclusion of the parabolic law. To achieve this, the Kudryashov method is used to obtain a group of dark solitons by applying the complex envelope and distinguishing between real and imaginary structures. Based on the results, the amplitude of the dark solitons can be easily controlled by adjusting the values of the nonlinear effects.
Article
Optics
K. Hosseini et al.
Summary: The main objective of this paper is to investigate the dynamics of soliton waves in a generalized nonlinear Schrodinger equation. The real and imaginary portions of the equation are first extracted using a complex wave transformation. Solitons and Jacobi elliptic structures of the governing model, describing the propagation of femtosecond pulses in nonlinear optical fibers, are then constructed through applying the modified Jacobi elliptic expansion method. In the end, it is shown that the width of bright and dark solitons respectively decreases and increases, while the amplitude of both waves decreases with the increase of nonlinear parameters through numerical representations.
Article
Engineering, Mechanical
J. Kalita et al.
Summary: In this study, the energy integral is derived using Sagdeev potential in a weakly relativistic plasma, leading to the discovery of compressive and rarefactive subsonic solitary waves in different propagation directions. It is found that compressive relativistic solitons have higher potential depths compared to non-relativistic solitons in all directions, allowing for denser plasma particles in the potential well. Furthermore, the study shows that the compressive soliton amplitude increases as the propagation direction gets closer to the magnetic field's direction.
NONLINEAR DYNAMICS
(2023)
Article
Telecommunications
Ahmed H. Arnous et al.
Summary: This paper studies the formation of dark and singular stationary optical solitons resulting from quadratic-cubic and generalized quadratic-cubic forms of nonlinear refractive index coupled with nonlinear chromatic dispersion. The temporal evolution is considered in both linear and generalized forms. The enhanced Kudryashov's approach enables the retrieval of such solitons.
Article
Engineering, Electrical & Electronic
Ali Murat Yalci et al.
Summary: The paper focuses on the retrieval of stationary soliton solutions to the complex Ginzburg-Landau equation using Jacobi's elliptic function approach, leading to soliton solutions under certain conditions.
OPTICAL AND QUANTUM ELECTRONICS
(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
Optics
Abdullah Sonmezoglu
Summary: In this paper, stationary optical solitons to nonlinear Schrodinger's equation with nonlinear chromatic dispersion and Kudryashov's quintuple power law nonlinearity are studied using the extended version of G'/G-expansion approach, resulting in various soliton solutions.
Article
Computer Science, Information Systems
Ahmed H. Arnous et al.
Summary: The study focuses on the application of the enhanced Kudryashov approach in dealing with the model of self-phase modulation, pointing out the limitations when the nonlinearity has a generalized form. In contrast to the common approach in the past, the current analysis employs a direct method rather than intermediate phase-portrait analysis.
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
Physics, Multidisciplinary
Mehmet Ekici
Summary: This study obtains stationary optical solitons for the complex Ginzburg-Landau equation by using Kudryashov's self-phase modulation structures. The nonlinearity of chromatic dispersion is also considered. Six forms of nonlinear refractive index are examined. The adopted integration scheme, the generalized G'/G-expansion approach, provides solutions in terms of Jacobi's elliptic functions. By applying the limiting approach with the modulus of ellipticity, stationary optical solitons finally emerge from the model.
Article
Astronomy & Astrophysics
Ahmed H. Arnous et al.
Summary: In this paper, stationary optical solitons with nonlinear chromatic dispersion are derived by considering a nonlocal form of nonlinearity and quintuple power-law of nonlinearity. The Kudryashov's integration scheme enables the retrieval of such solitons, leading to a plethora of solitons.
Article
Optics
Nikolay A. Kudryashov
Article
Optics
Abdullahi Rashid Adem et al.
Summary: We investigated stationary optical solitons in the LakshmananPorsezian-Daniel model, which includes nonlinear chromatic dispersion and a Kerr law of nonlinear refractive index. The solution is expressed in terms of a special function and its structure is described in details.
UKRAINIAN JOURNAL OF PHYSICAL OPTICS
(2021)
Article
Physics, Multidisciplinary
Abdullahi Rashid Adem et al.
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Optics
Anjan Biswas et al.
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Engineering, Mechanical
Anjan Biswas et al.
NONLINEAR DYNAMICS
(2011)
Article
Physics, Multidisciplinary
Zhenya Yan
Article
Physics, Multidisciplinary
Zhenya Yan
