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In this article, the parameter dynamics of super-Gaussian and super-sech pulses for the perturbed nonlinear Schrödinger's equation with polynomial and triple-power nonlinearity laws are recovered. The variational principle successfully recovers this dynamical system. [ABSTRACT FROM AUTHOR]

This paper obtains soliton solutions to Sasa–Satsuma equation, which is studied in birefringent fibers with multiplicative noise. The extended auxiliary equation approach reveals solutions in terms of Jacobi's elliptic functions from which bright, dark and singular solitons emerge when the limiting operation is applied to the modulus of ellipticity, with the limit approaching zero or unity. [ABSTRACT FROM AUTHOR]

The current paper recovers dispersive optical solitons in birefringent fibers that are modeled by the Schrödinger–Hirota equation with differential group delay and white noise. Itô Calculus conducts the preliminary analysis. The G ′ / G -expansion approach and the enhanced Kudryashov's scheme gave way to a wide spectrum of soliton solutions with the white noise component reflected in the phase of the soliton. [ABSTRACT FROM AUTHOR]

In this paper, we derive the solitons solutions to the cubic–quartic nonlinear Schrödinger equation (CQ-NLSE) in birefringent fibers with three laws of nonlinearity. These laws are parabolic law, quadratic-cubic law and non-local law. The new extended generalized Kudryashov method and our new method proposed for the first time have been applied. Many solutions have been found. Dark, bright and singular soliton solutions existed under constraint conditions. The comparative analysis of the two proposed methods shows that in the two cases of parabolic and non-local laws, the first method gives the dark and singular solitons in terms of tanh–coth hyperbolic functions, respectively, while the second method gives the bright and singular solitons in terms of sech–csch hyperbolic functions, respectively. But in the case of quadratic-cubic law, both methods give the bright-singular solitons in terms of sech 2 –csch 2 hyperbolic functions, respectively, with different arguments. [ABSTRACT FROM AUTHOR]

The current article studies optical solitons solutions for the dimensionless form of the stochastic resonant nonlinear Schrödinger equation (NLSE) with both spatio-temporal dispersion (STD) and inter-modal dispersion (IMD) having multiplicative noise in the itô sense. We will discuss seven laws of nonlinearities, namely, the Kerr law, power law, parabolic law, dual-power law, quadratic–cubic law, polynomial law, and triple-power law. The new auxiliary equation method is investigated. We secure the bright, dark, and singular soliton solutions for the model. [ABSTRACT FROM AUTHOR]

This paper obtains highly dispersive optical solitons in fiber Bragg gratings with the Kerr law of a nonlinear refractive index. The generalized Kudryashov's approach as well as its newer version makes this retrieval possible. A full spectrum of solitons is thus recovered. [ABSTRACT FROM AUTHOR]

We study for the first time perturbed optical solitons modelled using a Sasa-Satsuma equation involving a multiplicative noise. Two integration schemes retrieve soliton solutions to this model, which are described using parametric constraints. [ABSTRACT FROM AUTHOR]

This paper implements the sub-ODE method and a wide spectrum of solitons are recovered for Kudryashov's law of refractive index. The self-phase modulation comprises of four nonlinear components of refractive index. The perturbation terms are all of Hamiltonian type and are considered with maximum intensity. The solutions are written in terms of Weierstrass' elliptic functions and Jacobi's elliptic function. With the modulus of ellipticity approaching zero or unity, soliton solutions emerge. [ABSTRACT FROM AUTHOR]

We recover the cases of solutions in the shape of bright, dark and singular optical solitons for the self-phase modulation effect, which belongs to the type of N. A. Kudryashov's sextic power-law nonlinearity of refractive index. Three different integration schemes have been implemented. These are a unified Riccati equation, our new mapping scheme and our addendum to the common N. A. Kudryashov's method. All of the solitons are enlisted and the criterions of their existence are mentioned. Finally, we extract three appropriate conservation laws. [ABSTRACT FROM AUTHOR]

This paper studies couplers in optical metamaterials that come with power law of nonlinear refractive index. The Kudryashov's approach reveals bright, singular as well as bright-singular straddled optical soliton solutions. Both twin-core couplers and multiple-core couplers are studied. [ABSTRACT FROM AUTHOR]

New extended generalized Kudryashov method is proposed in this paper for the first time. Many solitons and other solutions of three nonlinear partial differential equations (PDEs), namely, the (1+1)-dimensional improved perturbed nonlinear Schrödinger equation with anti-cubic nonlinearity, the (2+1)-dimensional Davey–Sterwatson (DS) equation and the (3+1)-dimensional modified Zakharov–Kuznetsov (mZK) equation of ion-acoustic waves in a magnetized plasma have been presented. Comparing our new results with the well-known results are given. Our results in this article emphasize that the used method gives a vast applicability for handling other nonlinear partial differential equations in mathematical physics. [ABSTRACT FROM AUTHOR]

The current paper studies gap solitons with parabolic-nonlocal form of self-phase modulation. The soliton solutions for this model are revealed with the successful application of the extended auxiliary equation approach. The parameter constraints ensure the existence of such gap solitons. [ABSTRACT FROM AUTHOR]

The present paper derives highly dispersive soliton solutions in a coupler from optical metamaterials with Kerr law of nonlinear refractive index. In nonlinear optics and photonics, these wave packets possess a unique property, allowing them to sustain their shape and velocity during propagation through nonlinear media. Optical couplers utilizing metamaterials are advanced devices tailored to enhance the coupling and transfer of optical signals between different optical components or systems by harnessing the unique characteristics of these specially engineered materials. The paper's novelty lies in considering highly dispersive optical solitons that can be studied in optical couplers constructed from metamaterials. This paper's primary goal is to integrate a governing model concerning highly dispersive solitons in optical couplers with the incorporation of metamaterials. Therefore, the unified Riccati equation expansion procedure and the enhanced Kudryashov's scheme are adopted. They are being applied to such a device for the first time. These yield a full spectrum of optical solitons as well as straddled solitons. The novelty lies in the joint application of the two procedures, which uncovers various solitons. Furthermore, one of the approaches uncovers an unexpected benefit by revealing straddled soliton solutions. [ABSTRACT FROM AUTHOR]

In this article, the modified extended tanh-function method is employed to solve fractional partial differential equations in the sense of the modified Riemann–Liouville derivative. Based on a nonlinear fractional complex transformation, certain fractional partial differential equations can be turned into nonlinear ordinary differential equations of integer orders. For illustrating the validity of this method, we apply it to four nonlinear equations namely, the space–time fractional generalized nonlinear Hirota–Satsuma coupled KdV equations, the space–time fractional nonlinear Whitham–Broer–Kaup equations, the space–time fractional nonlinear coupled Burgers equations and the space–time fractional nonlinear coupled mKdV equations. [ABSTRACT FROM AUTHOR]

This research explores the intriguing realm of eighth-order embedded solitons in highly dispersive media with cubic–quartic nonlinear susceptibilities χ(2) and χ(3), all within the dynamic context of multiplicative white noise and the framework of Itô calculus. Two different approaches are used in this study. The new auxiliary equation approach produces the bright soliton and singular soliton solutions, while the addendum Kudryashov’s approach produces the bright soliton, singular soliton and combo bright–singular soliton solutions. The system under investigation and the results documented within this work stand as pioneering and original contributions to the field of nonlinear optics. Furthermore, a collection of 2D, 3D and contour plots is produced to visually represent the spatial distribution and progression of different solutions. This not only contributes to the advancement of nonlinear equations in theory but also offers valuable insights for practical applications. [ABSTRACT FROM AUTHOR]

In this comment, we show by simple calculation that the new auxiliary equation method (Khater method) used in the above paper is absolutely wrong. Consequently, all the exact solutions of the proposed nonlinear equation obtained in the above paper are also wrong. [ABSTRACT FROM AUTHOR]

This study delves into the realm of optical soliton solutions within the intricate framework of highly dispersive couplers integrated with optical metamaterials featuring a parabolic law nonlinear refractive index. Employing the extended auxiliary equation method, the investigation systematically unveils various soliton solutions, including dark solitons, bright solitons, singular solitons, and a distinctive amalgamation of bright and singular solitons. The results illuminate the diverse dynamics of solitons in these complex systems, offering crucial insights into the interplay among dispersion, nonlinearity, and metamaterial characteristics. Beyond enhancing the theoretical understanding of soliton behavior in optical metamaterial couplers, the findings hold practical significance by potentially influencing the design and optimization of optical communication devices and systems. [ABSTRACT FROM AUTHOR]