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In this work, we derived the (2+1)-dimensional Schrödinger equation from the (2+1)-dimensional Klein–Gordon equation. We also obtained the fractional order form of this equation at the same time so as to discover the connection between them. For the (2+1)-dimensional Klein–Gordon equation, symmetries and conservation laws are pres ented. For different gauge constraint, from the perspective of conservation laws, the corresponding symmetries are obtained. After that, based on the fractional complex transform, soliton solutions of the time fractional (2+1)-dimensional Schrödinger equation are displayed. Some figures are showed behaviors of soliton solutions. It is important to discover the relationships between these equations and to obtain their explicit solutions. These solutions will perhaps provide a theoretical basis for the explanation of complex nonlinear phenomena. From the results of this paper, it is clear that the Lie symmetry method is a particularly important tool for dealing with differential equations. [ABSTRACT FROM AUTHOR]

This work is a sequel to the previously reported results on stationary optical solitons with several forms of Kudryashov's law of self-phase modulation. The study is conducted with generalized temporal evolution by the aid of extended trial function approach. The solutions that naturally emerged from this scheme are in terms of Jacobi's elliptic function which finally led to stationary solitons with the modulus of ellipticity approaching its appropriate limit. [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]

This paper carries out numerical simulations of highly dispersive optical solitons with differential group delay having quadratic-cubic law of nonlinearity. The Laplace–Adomian decomposition scheme is implemented to visualize the soliton propagation dynamics. Both bright and dark solitons are addressed. The error measure for these numerical approximations is impressively low as presented. [ABSTRACT FROM AUTHOR]

This work recovers cubic–quartic soliton solutions to the Lakshmanan–Porsezian–Daniel model by the method of undetermined coefficients. Both polarization-preserving fibers and birefringent fibers are studied. The conservation laws for polarization-preserving fibers are also retrieved and enumerated. The existence criteria for the displayed solitons are also presented. [ABSTRACT FROM AUTHOR]

This paper studies polarized cubic–quartic solitons that are modeled by Fokas–Lenells equation in birefringent fibers. Two integration schemes recovered a spectrum of soliton solutions to the model. Subsequently, the bright solitons compute the corresponding conserved quantities from the respective densities that are recovered by the multiplier approach. [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]

This paper retrieves soliton solutions to fiber Bragg ratings with dispersive reflectivity where cubic–quartic dispersive effects are considered as opposed to the usual chromatic dispersion. The auxiliary equation approach and an addendum to Kudryashov's scheme display a complete spectrum of soliton forms to the model that is studied with Kerr effect. [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]

This paper addresses the dynamics of optical solitons in the presence of perturbation terms by the aid of three integration schemes. They are modified simple equation method, trial equation scheme, and the extended trial equation scheme. There are three types of nonlinearities that are studied in this paper which are Kerr law, power law, and logarithmic law. The constraint conditions for the existence of these solitons are also presented. [ABSTRACT FROM AUTHOR]

This paper employs extended trial equation method to retrieve nematicons in liquid crystals from its governing equation. In addition, several other forms of solution naturally emerged from the integration algorithm. These are shock waves, singular solitons, snoidal waves, periodic singular waves, plane waves and others. These variety of solutions are being reported for the first time in the context of liquid crystals. [ABSTRACT FROM AUTHOR]

This paper addresses solitons in optical metamaterials. The semi-inverse variational principle (SVP) is utilized to secure bright soliton solutions to the governing model. There are five forms of nonlinearity that are studied in this paper. They are Kerr law, power law, parabolic law, dual-power law and finally the log law nonlinearity. In particular for Kerr law nonlinearity, there are two additional forms of soliton solutions obtained. They are cosh-Gaussian pulses and bright-dark combo solitons and these are collectively being referred to as exotic solitons. There are several constraint conditions that naturally emerge for these solitons to exist. [ABSTRACT FROM AUTHOR]

This paper obtains soliton solutions in optical couplers. The governing equation is solved by the aid of G′/G-expansion scheme. There are four types of nonlinear media that are taken into consideration. These are Kerr law, power law, parabolic law, and dual-power law. There are two kinds optical couplers studied in this paper. They are twin-core couplers and multiple-core couplers, where coupling with nearest neighbors as well as coupling with all neighbors are considered. Dark and singular soliton solutions are retrieved. These soliton solutions come with constraint conditions that must hold for the solitons to exist. [ABSTRACT FROM AUTHOR]

This paper obtains bright, dark and singular soliton solutions to dense wavelength division multiplexed (DWDM) system, with spatio-temporal dispersion. There are two types of nonlinear media that are considered and they are Kerr law and parabolic law. Four integration algorithms are applied to retrieve these solitons. They are G′/G-expansion scheme, extended tanh function approach, Kudryashov's algorithm and finally the ansatz method. The results follow with respective constraints that guarantees the existence of solitons. [ABSTRACT FROM AUTHOR]

The dynamics of dispersive optical solitons, modeled by Schrödinger-Hirota equation, are studied in this paper. Bright, dark and singular optical soliton solutions to this model are obtained in presence of perturbation terms that are considered with full nonlinearity. Soliton perturbation theory is also applied to retrieve adiabatic parameter dynamics of bright solitons. Optical soliton cooling is also studied. Finally, exact bright, dark and singular solitons are addressed for birefringent fibers with perturbation terms included. [ABSTRACT FROM AUTHOR]

This paper studies the dynamics of optical solitons in multi-dimensions with spatio-temporal dispersion and non-Kerr law nonlinearity. The integrability aspect is the main focus of this paper. Five different forms of nonlinearity are considered - Kerr law, power law, parabolic law, dual-power law and log law nonlinearity. The traveling wave hypothesis, ansatz approach and the semi-inverse variational principle are the integration tools that are adopted to retrieve the soliton solutions to the governing equation. As a result, several constraint conditions arise out of the integration process and represent necessary conditions for the existence of solitons. [ABSTRACT FROM AUTHOR]

This paper obtains the 1-soliton solution by the ansatz method for the proposed model that governs the propagation of solitons through the neurons. This model is an improved one that describes the solitons in neurosciences more accurately. The ansatz method is applied to obtain the 1-soliton solution to the model. The Lie symmetry analysis is subsequently applied to obtain the conservation laws for the model. [ABSTRACT FROM AUTHOR]

This paper studies the perturbation of the improved version of the nonlinear Schrödinger's equation that governs the propagation of solitons through nonlinear optical fibers. The semi-inverse variational principle is employed in order to obtain an analytical soliton solution in presence of the perturbation terms. There are three types of nonlinearity that will be studied. They are Kerr law, power law and the log law. The constraint conditions will naturally fall out in order for the soliton solutions to exist. The numerical simulations supplement the analytical results for each of the three laws of nonlinearity. [ABSTRACT FROM AUTHOR]

In this paper, the governing equation for optical solitons, namely the nonlinear Schrödinger's equation, is studied with non-Kerr law nonlinearity in the presence of perturbation terms with full nonlinearity. The quasi-stationary optical soliton is obtained after applying the multiple-scale perturbation analysis. The forms of nonlinearity that are studied in this paper are Kerr law, power law and the log law. [ABSTRACT FROM AUTHOR]

This paper obtains the stationary optical 1-soliton solution of the nonlinear Schrödinger's equation with dual-power law nonlinearity. The technique of Lie symmetry is used to obtain the solution. [ABSTRACT FROM AUTHOR]

This paper talks about obtaining an exact 1-soliton solution of the generalized Radhakrishnan, Kundu, Lakshmanan equation with nonlinear dispersion. The solitary wave ansatz will be used to carry out the integration. It will be proved that dark optical solitons can exist only when the power law nonlinearity reduces to Kerr law. [ABSTRACT FROM AUTHOR]

This paper obtains the parameter dynamics of super-sech optical solitons propagating through optical fibers. The variational principle is applied to obtain these parameter dynamics. Both polarization preserving fibers as well as birefringent fibers are studied in this paper. The study is then finally extended to the case of DWDM systems. The adiabatic parameter dynamics of soliton parameters is then obtained in the presence of perturbation terms. The numerical simulations are also obtained to complete the analysis. [ABSTRACT FROM AUTHOR]

This paper studies the propagation of solitons through optical fibers with dispersion management. The adiabatic variation of the soliton parameters, due to the presence of perturbation terms, is obtained. The dynamics is studied for the case of polarization-preserving fibers, while the types of pulses that are considered here are Gaussian, super-Gaussian and supersech. The perturbation terms that are taken into consideration are both local and nonlocal. [ABSTRACT FROM AUTHOR]

The dynamics of optical solitons, with dispersion management, propagating through a dense wavelength-division-multiplexed system with damping and amplification is studied. The adiabatic parameter dynamics of the solitons in the presence of perturbation terms have been obtained by virtue of the variational principle. In particular, the Gaussian and super-Gaussian pulses have been considered. [ABSTRACT FROM AUTHOR]

The dynamics of optical solitons with dispersion-management propagating through optical fibers with damping and amplification is studied. A multiple-scale perturbation expansion method is used to analyze the nonlinear Schrödinger's equation that governs the propagation of such solitons. In this paper we have considered both polarization preserving as well as birefringent fibers. Finally, the case of dense wavelength-division-multiplexed soliton system is also considered. [ABSTRACT FROM AUTHOR]

The soliton perturbation theory is employed to study chirped solitons that propagate through optical couplers and is governed by the dispersion-managed nonlinear Schrödinger's equation. Here, in this paper, we have considered both kinds of couplers namely twin-core as well as the multiple-core type. In either case, both Gaussian and super-Gaussian solitons are taken into account. [ABSTRACT FROM AUTHOR]

The propagation of solitons through multiple-core nonlinear fiber couplers for non-Kerr law nonlinearity is studied in this paper. The parameter dynamics of such solitons has been obtained. In particular, we have considered the ring geometry for the arrangement of fiber arrays. [ABSTRACT FROM AUTHOR]

The variational principle is employed to obtain the parameter dynamics of a superGaussian chirped soliton that propagates through birefringent optical fibers and is governed by the dispersion-managed vector nonlinear Schrödinger's equation. The waveform deviates from that of a classical soliton. The periodically changing strong chirp of such a soliton reduces the effective nonlinearity that is necessary for balancing the local dispersion. This study is extended to obtain the adiabatic evolution of the parameters of such a soliton in presence of perturbation terms. [ABSTRACT FROM AUTHOR]

In an optical communication system it is necessary to place the solitons close to one another to increase the information carrying capacity of the fiber. The theory of soliton–soliton interaction in a fiber optic communication system, through a single channel, is studied in this paper. In presence of the perturbation terms, the two soliton interaction of the Nonlinear Schrödinger's Equation is investigated. It is analytically proved and numerically supported that the perturbation terms lead to the suppression of the interaction of solitons through an optical fiber. [ABSTRACT FROM AUTHOR]

The propagation of solitons through an optical fiber, described by the perturbed Nonlinear Schrödinger's equation, is studied in this paper by the method of Multiple Scale Perturbation Expansion. Here, it is shown for the first time that, by introducing a new definition of the phase of soliton, one can obtain corrections to the pulse, in presence of the perturbation terms, where the standard soliton perturbation theory fails. This dynamically stable soliton is a very useful physical model in the optical soliton communication world. A comparison is made with results obtained by other methods along with numerical simulations. [ABSTRACT FROM AUTHOR]