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This paper employs the Lie symmetry analysis to integrate the concatenation model studied with the Kerr law of self-phase modulation. The reduced ordinary differential equation is integrated using two approaches, which are the extended tanh method and the generalized Arnous' approach. These yielded dark and singular solitons for the model. [ABSTRACT FROM AUTHOR]

The current paper recovers cubic–quartic optical solitons in fiber Bragg gratings having polynomial law of nonlinear refractive index structures. Lie symmetry analysis is carried out, starting with the basic analysis. Then, it is followed through with improved Kudryashov and generalized Arnous schemes. The parameter constraints are also identified for the existence of such solitons. Numerical surface plots support the adopted applied analysis. [ABSTRACT FROM AUTHOR]

The paper revisits highly dispersive optical solitons that are addressed by the aid of Lie symmetry followed by the implementation of the Riccati equation approach and the improved modified extended tanh-function approach. The soliton solutions are recovered and classified. The conservation laws are also recovered and the corresponding conserved quantities are enlisted. [ABSTRACT FROM AUTHOR]

This paper implements two of Kudryashov's approaches to extract optical soliton solutions to the concatenation model that is a conjunction of the nonlinear Schrödinger's equation, Lakshmanan-Porsezian-Daniel model, and the Sasa-Satsuma equation. A full spectrum of soliton solutions emerged along with the parameter constraints that are all comprehensively presented. [ABSTRACT FROM AUTHOR]

This work recovers cubic-quartic optical solitons with dispersive reflectivity in fiber Bragg gratings and parabolic law of nonlinearity. The Lie symmetry analysis first reduces the governing partial differential equations to the corresponding ordinary differential equations which are subsequently integrated. This integration is conducted using two approaches which are the modified Kudryashov's approach as well as the generalized Arnous' scheme. These collectively yielded a full spectrum of cubic-quartic optical solitons that have been proposed to control the depletion of the much-needed chromatic dispersion. They range from bright, dark, singular to combo solitons. These solitons are considered with dispersive reflectivity, which maintains the necessary balance between chromatic dispersion and nonlinear refractive index structure for an uninterrupted transmission of solitons along intercontinental distances. Their respective surface and contour plots are also exhibited. A few closing words are included with some prospective future avenues of research to extend this topic further. [ABSTRACT FROM AUTHOR]

This research finds an equation in a continuous domain and a discrete equation governing the system of cold bosonic atoms (CBA) in a zigzag optical lattice using a continuum approximation. Many solutions to the equation were obtained using two distinct methods: the three-wave approach (multi-wave interaction, rational solutions, and rational solution interaction) and the extended sub-equation method. These analytical approaches are more effective, consistent, and comprehensive mathematical tools for obtaining various exact closed-form solutions for a wide range of fractional space-time nonlinear evolution equations encountered in optical physics, condensed matter physics, and plasma physics. The solutions generated are in the form of hyperbolic and trigonometric solutions, and other-form solutions are obtained. Three-dimensional graphics and contour plots are often used to depict the graphical representations of the combined soliton solutions. These findings will aid our understanding of the dynamics of the zigzag optical grids and many other structures formed by colder bosonic atoms. The applied approaches are more simple, efficient, and straightforward to obtain the closed-form solutions for various nonlinear evolution equations in the fields of nonlinear sciences and physical engineering. [ABSTRACT FROM AUTHOR]

In this work, the new optical soliton solutions and interaction solutions for the space-time fractional Fokas–Lenells equation with fractional M -derivatives are constructed via three mathematical analytical techniques, namely the extended SE method, unified solver method, and three-wave methods. The results have proved the efficiency of the suggested techniques for obtaining abundant optical soliton solutions to nonlinear evolution equations (NLEEs) and closed-form solutions in the forms of rational function solutions; hyperbolic and trigonometric function solutions and multi-wave interaction solutions are obtained. These techniques are more efficient, robust, and powerful mathematical tools for acquiring several optical soliton solutions for many other fractional space-time NLEEs that arise in optical physics and plasma physics. The graphical representations of the combined optical solitons are demonstrated using three- and two-dimensional graphics. [ABSTRACT FROM AUTHOR]

In this work, symmetry reduction for nonlinear Schrödinger's equation with anti-cubic nonlinearity is determined by using the invariance of equations under Lie group of transformations. Using the similarity transformations the equation is reduced into system of ordinary differential equations. Corresponding to reduced ordinary differential equations, some exact solutions are obtained. These yields bright solitons, dark solitons, singular solitons and other explicit solutions. It is also pointed out that some of the results reported earlier are particular forms of current solutions. [ABSTRACT FROM AUTHOR]

This work introduces a new generalized integration scheme to construct the pure-cubic optical solitons in a polarization-preserving fiber with Kerr law nonlinearity. First, Lie symmetry analysis is performed to find the similarity transformation. Then, the exact solutions of the governing equation are derived via a purposed new generalized integration scheme. In particular, we have derived the pure-cubic dark, singular and combo dark-singular soliton solutions. The existence criteria of such solutions are also provided. [ABSTRACT FROM AUTHOR]

This paper employs Lie symmetry analysis to recover cubic–quartic optical soliton solutions to the Lakshmanan–Porsezian–Daniel model in birefringent fibers. The results are a sequel to the previously reported work on the same model in unpolarized fibers. Dark, singular, and straddled optical solitons that emerged from the scheme are presented. [ABSTRACT FROM AUTHOR]

• The cubic–quartic Lakshmanan–Porsezian–Daniel equation is studied. • Lie symmetry analysis is used. • The straddled singular–bright optical solitons are reported. This study obtains straddled singular–bright optical solitons to cubic–quartic Lakshmanan–Porsezian–Daniel equation by Lie symmetry analysis. The reduced ordinary differential equations are handled using Kudryashov's method. [ABSTRACT FROM AUTHOR]

In this work, Kudryashov's equation with third-order dispersion and fourth-order dispersion was studied via Lie symmetry analysis. First, similarity transformation helps us to converted governing equation into a system of ordinary differential equations. Then hyperbolic-expansion method and Kudryashov method reveals the cubic-quartic optical soliton solutions in the form of dark, bright, singular and combo bright-singular soliton solutions. [ABSTRACT FROM AUTHOR]

Lie symmetry analysis handled the nonlinear Schrödinger's equation that is studied with generalized anti-cubic nonlinear form. These yielded bright, dark and singular optical soliton solutions as well as a bright-singular combo optical soliton solution to the model. The restrictions on the parameters for the existence of such solitons are also presented. OCIS Codes: 060.2310; 060.4510; 060.5530; 190.3270; 190.4370 [ABSTRACT FROM AUTHOR]

The present study derives cubic–quartic optical solitons in fiber Bragg gratings having Kerr law of nonlinearity along with dispersive reflectivity. The Lie symmetry analysis collapses the coupled partial differential equations to a coupled set of ordinary differential equations. They are subsequently solved to recover singular and dark solitons to the model. The numerical simulations support the analytical findings. [ABSTRACT FROM AUTHOR]

The current paper addresses the bifurcation analysis and sketches the phase portraits of the dynamical system that emerged from fiber Bragg gratings structure due to parabolic–nonlocal combo nonlinearity. The Lie symmetry analysis led to the corresponding ordinary differential equations that were subsequently analyzed. [ABSTRACT FROM AUTHOR]