Parabolic Law Nonlinearity Research Articles

Optical solitons with differential group delay and four-wave mixing using two integration procedures

Optical solitons in birefringent fibers with the effect of four-wave mixing having both parabolic and Kerr law nonlinearity are obtained by the modified simple equation scheme and the trial equation approach. Dark, bright as well as singular soliton type solutions are derived. Also, the two integration schemes give rise to additional solutions such as singular periodic solutions.

Optical solitons in birefringent fibers with weak non-local nonlinearity and four-wave mixing by extended trial equation method

This paper studies optical solitons in birefringent fibers with parabolic law nonlinearity coupled with waekly non-local nonlinear medium. The four-wave mixing effect is taken into consideration and thus retrieval of soliton solutions would require phase-matching condition.

Solitons in optical metamaterials having parabolic law nonlinearity with detuning effect and Raman scattering

The dynamics of pulse propagation through nonlinear optical metamaterials, maintaining parabolic law nonlinearity, is investigated. The model includes spatio-temporal dispersion, detuning effect, inter-modal dispersion, self-steepening effect, Raman scattering, nonlinear dispersion and third-order dispersion. Bright, dark and singular soliton solutions are derived by the implementation of coupled phase-amplitude formulation. The conditions on the material parameters for the existence of these solitons are also enumerated.

Optical solitons of Lakshmanan–Porsezian–Daniel model with a couple of nonlinearities

The aim of this article is to present exact optical solutions of three forms of Lakshmanan–Porsezian–Daniel model. They are the Kerr law, parabolic law and anti-cubic law nonlinearity. The sine-Gordon expansion method is applied to extract exact optical solutions. It is shown that Sine-Gordon expansion method provides us with a powerful mathematical tool for solving nonlinear partial differential equations in mathematical physics.

The $$\phi ^{6}$$ ϕ 6 -model expansion method for solving the nonlinear conformable time-fractional Schrödinger equation with fourth-order dispersion and parabolic law nonlinearity

The $$\phi ^{6}$$ -model expansion method combined with the conformable time-fractional derivative is applied in this paper for finding many new exact solutions including Jacobi elliptic function solutions, solitary wave solutions, trigonometric function solutions and other solutions to the nonlinear conformable time-fractional Schrodinger equation with fourth-order dispersion and parabolic law nonlinearity. This method presents a wider applicability for handling the nonlinear partial differential equations. Comparing our results with the well-known results are given.

Hamiltonian perturbation of optical solitons with parabolic law nonlinearity using three integration methodologies

This work secures optical soliton solution to the nonlinear Schrodinger’s equation that appears with parabolic law nonlinearity and a couple of Hamiltonian type perturbation terms that are strong. Three integration schemes retrieve soliton solutions to the model. They are csch-function method, tanh-coth algorithm and modified simple equation technique.

Optical solitons with differential group delay by trial equation method

This paper secures bright, dark and singualr soliton solutions in birefringent fibers. Both Kerr law and parabolic law nonlinearity are studied. The trial equation method successfully retrieves these solitons with constraint relations that assure their existence.

Chirped solitons in optical metamaterials with parabolic law nonlinearity by extended trial function method

This paper secures chirped bright and singular soliton solutions in an optical metamaterial that is considered with parabolic law nonlinearity and self-steepening effect. The extended trial function method is the integration scheme adopted in this paper. Several other solutions such as singular periodic waves and elliptic functions naturally emerge as a byproduct of this scheme.

Solitary wave solutions of time–space nonlinear fractional Schrödinger’s equation: Two analytical approaches

This paper obtains analytical solution of nonlinear Schrödinger equation in both time and space fractional terms. Two analytical approaches, Nucci’s reduction method and simplest equation method are utilized to extract analytical solutions specially of soliton kinds. The Kerr law, power law, parabolic law, dual-power law and log law nonlinearities are considered separately.

(2 + 1)-dimensional bright optical solitons in metamaterials with Kerr, power and parabolic law nonlinearities

In this paper, we investigate the dynamics of bright optical solitons in nonlinear metamaterials governed by a (2 + 1)-dimensional nonlinear Schrödinger equation. Three types of nonlinearities have been considered, Kerr law, power law and parabolic law. We based on the solitary wave ansatz method to find these optical soliton solutions. All necessary parametric conditions for their existence are driven.

Analytical soliton solutions of Biswas–Milovic equation in Kerr and non-Kerr law media

Biswas and Milovic presented a summed up or generalized model for the NLSE that records for a few defects in the fiber amid long separation transmission of these heartbeats or pulses. This article concentrates the exact arrangement of the Biswas and Milovic equation with Kerr law, parabolic law, power law and dual power law nonlinearity by another effective method. This paper concentrates the irritated Biswas–Milovic condition by the guide of the Exp (−φ(ε))-expansion strategy. We report additionally correct travelling wave solutions in a brief shape to the Biswas–Milovic condition which concedes physical centrality in applications. The acquired outcomes demonstrate that the Exp (−φ(ε))-expansion method is clear scientific device for seeking systematic or analytic solutions with discretionary or material parameters of higher-dimensional nonlinear partial differential equations. The results procured uncover that the technique is unequivocal or explicit, successful and simple to utilize.

Beta-derivative and sub-equation method applied to the optical solitons in medium with parabolic law nonlinearity and higher order dispersion

By using the sub-equation method, we construct the analytical solutions of the space-time generalized nonlinear Schrödinger equation involving the beta-derivative. This equation describing the propagation of ultra-short optical solitons through parabolic law medium. Nonlinear perturbations of higher-order and self-steepening terms are taken into account. As a result, some new exact solutions are constructed under constraint conditions.

Abundant soliton solutions of the resonant nonlinear Schrödinger equation with time-dependent coefficients by ITEM and He’s semi-inverse method

The improved $$\tan (\phi /2)$$ -expansion method (ITEM) and He’s semi-inverse variational method (HSIVM) are the efficient methods for obtaining exact solutions of nonlinear differential equations. In this paper, the ITEM and HSIVM are applied to construct exact solutions of the resonant nonlinear Schrodinger equation (RNLSE) with time-dependent coefficients for parabolic law nonlinearity. The resonant nonlinear Schrodinger equation plays a very important role in mathematical physics and nonlinear optics. We compare analytical findings with the results of the other analytical schemes describing the ansatz method approach and expansion method are used to carry out the integration. Description of the ITEM is given and the obtained results reveal that the ITEM is a new significant method for exploring nonlinear partial differential models. Moreover, by help of the HSIVM we obtained the bright and dark soliton wave solutions. Finally, by using Matlab, some graphical simulations were drawn to see the behavior of these solutions.

Optical soliton perturbation with parabolic and dual-power law nonlinearities by semi-inverse variational principle

This paper secures bright optical soliton solutions to the nonlinear Schrödinger's equation with parabolic and dual-power law nonlinearities. This model carries Hamiltonian type perturbation terms that permit integrability. The semi-inverse variational principle is the integration criteria for this perturbed model and the soliton structure is chosen to be a different one from earlier reported works.

Thirring dipole solitons in birefringent optical fibers with spatio-temporal dispersion, four-wave mixing and non-Kerr law nonlinearities

In this paper, we investigate, for the first time, Thirring dipole solitons in birefringent optical fibers with Kerr and parabolic law nonlinearities in the presence of spatio-temporal dispersion and four-wave mixing terms. Based on a complex wave ansatz, we solved analytically tow variant of the vector coupled nonlinear Schrödinger equation. All the necessary parametric conditions for the existence of the Thirring dipole solitons are extracted.

Electromagnetic wave solitons in optical metamaterials

In this paper, we investigate the nonlinear Schrödinger equation governing the dynamics of electromagnetic pulse in metamaterials exhibiting a parabolic law nonlinearity. By using the complex envelope ansatz method and the F-expansion method, we obtain bright and dark soliton as well as kink, bell shape solitary wave solutions and periodic wave solutions. These new exact solutions may be useful in the explanation and understanding of metamaterials physical structure and phenomena.

Solitons and other exact solutions for a class of nonlinear Schrödinger-type equations

Recently, Zayed and Alurrfi have applied an extended auxiliary equation method for constructing the exact solutions of three nonlinear partial differential equations (PDEs) via the (2+1)-dimensional nonlinear cubic-quintic Ginzburg–Landau equation, the (1+1)-dimensional resonant nonlinear Schrödinger's equation with parabolic law nonlinearity and the (1+1)-dimensional nonlinear generalized Zakharov system of equations. In this article we apply a different method called a new mapping method proposed by Zeng and Yong for finding many other new exact solutions for the same three nonlinear PDEs mentioned above. Comparing the solutions resulting from these two different methods are given. The obtained results confirm that both the extended auxiliary equation method and the new mapping method are efficient techniques for analytic treatments of a wide variety of nonlinear PDEs in mathematical physics.

Optical solitons with time fractional nonlinear Schrödinger equation and competing weakly nonlocal nonlinearity

The optical solitons have been extracted from the model that describes the dynamics of solitons in nonlinear optics with competing weakly nonlocal nonlinearity. The diffraction coefficient and parabolic law nonlinearity are also consider in this time fractional model. The constraint conditions, for the existence of the dark and singular soliton solutions, are also listed. Additionally, a couple of other solutions known as singular periodic solutions, fall out as a by-product of this scheme.

Optical solitons with higher order dispersions in parabolic law medium by trial solution approach

This paper obtains bright, dark and singular soliton solutions in optical fibers with parabolic law nonlinearity in the presence of third and fourth order dispersions. The trial solutions approach is employed to carry out this integration. Besides solitons, periodic singular solutions are also obtained as a byproduct. The corresponding constraint conditions are also listed.

Chirped Optical Solitons in Birefringent Fibers with Parabolic Law Nonlinearity and Four-Wave Mixing

Chirped Optical Solitons in Birefringent Fibers with Parabolic Law Nonlinearity and Four-Wave Mixing