Kerr Law Nonlinearity Research Articles

Optical solitons with Lakshmanan–Porsezian–Daniel model by modified extended direct algebraic method

This paper obtains bright and dark–singular combo solitons for the Lakshmanan–Porsezian–Daniel model by the aid of modified extended direct algebraic method. Both Kerr law and power law nonlinearities are considered. However, it is only the case of Kerr law that led to soliton solutions. Some additional solutions also emerged and they are singular periodic waves and elliptic functions.

Dark and singular optical solitons for the conformable space-time nonlinear Schrödinger equation with Kerr and power law nonlinearity

This paper extracts novel dark and singular optical solitons for the conformable space time nonlinear Schrödinger equation (CSTNLSE) with Kerr and power law nonlinearity by two integration schemes. The integration schemes are generalized tanh (GT), and Bernoulli (BL) sub-ODE methods. The constraints conditions for the existence of solitons are reported. The newly introduced fractional derivative called conformable derivative is used for extracting the soliton solutions. Numerical simulations of some of the obtained solutions are also presented.

Soliton solutions of fractional complex Ginzburg–Landau equation with Kerr law and non-Kerr law media

In this study, new soliton solutions of the fractional complex Ginzburg–Landau equation, that models soliton propagation in the presence of detuning factor, have been constructed. The Kerr law, power law, dual-power law and log law nonlinearity have been considered. The exp(−ϕ(ξ))-expansion method has been utilized for finding new exact solutions of fractional complex Ginzburg–Landau equation. Different forms of solutions, including the hyperbolic, trigonometric and rational function solutions are formally extracted. The method suggests a useful and efficient technique to look for the exact solutions of a wide range of nonlinear fractional partial differential equations.

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.

Fractional analysis for nonlinear electrical transmission line and nonlinear Schroedinger equations with incomplete sub-equation

We use the fractional complex transform with the modified Riemann-Liouville derivative operator to establish the exact and generalized solutions of two fractional partial differential equations. We determine the solutions of fractional nonlinear electrical transmission lines (NETL) and the perturbed nonlinear Schroedinger (NLS) equation with the Kerr law nonlinearity term. The solutions are obtained for the parameters in the range ( $0<\alpha\le 1$ ) of the derivative operator and we found the traditional solutions for the limiting case of $\alpha =1$ . We show that according to the modified Riemann-Liouville derivative, the solutions found can describe physical systems with memory effect, transient effects in electrical systems and nonlinear transmission lines, and other systems such as optical fiber.

Optical solitons and group invariant solutions to Lakshmanan–Porsezian–Daniel model in optical fibers and PCF

The Lie symmetry analysis is applied to Lakshmanan–Porsezian–Daniel model, with Kerr and power law nonlinearity, to retrieve optical soloiton solutions. Singular soliton solutions are available by the application of this algorithm.

Optical solitons with Lakshmanan–Porsezian–Daniel model using a couple of integration schemes

This paper retrieves dark and singular optical soliton solutions to the Lakshmanan–Porsezian–Daniel equation for Kerr law nonlinearity by using two integration schemes. These are extended Jacobi's elliptic function approach and exp(−Φ(η))–expansion method. The existence criteria for these solitons are also obtained that are presented as constraint conditions. As a byproduct, periodic singular solutions are recovered and these too are listed in the paper.

Soliton Solutions of the Coupled Schrödinger-Boussinesq Equations for Kerr Law Nonlinearity

In this paper, the coupled Schrödinger-Boussinesq equations (SBE) will be solved by the sech, tanh, csch, and the modified simplest equation method (MSEM). We obtain exact solutions of the nonlinear for bright, dark, and singular 1-soliton solution. Kerr law nonlinearity media are studied. Results have proven that modified simple equation method does not produce the soliton solution in general case. Solutions may find practical applications and will be important for the conservation laws for dispersive optical solitons.

Exact solutions of perturbed nonlinear Schrödinger’s equation with Kerr law nonlinearity by improved $${\textbf{tan}} \left( {\frac{{\boldsymbol{\phi}} \left( {\boldsymbol{\xi}} \right)}{{\textbf{2}}}} \right)$$tanϕξ2-expansion method

This paper carries out exact solutions of the perturbed nonlinear Schodinger’s equation withy Kerr law nonlinearity by using the improved tan $$\left( {\frac{\phi \left( \xi \right)}{2}} \right)$$ -expansion method. The exact solutions contain four types: hyperbolic function solution, trigonometric function solution, exponential solution, and rational solution. The method appears to be easier and faster by means of symbolic computational system and can be applied to the other nonlinear evolution equations in mathematical physics.

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.

Optical Gaussons and dark solitons in directional couplers with spatiotemporal dispersion

This paper study the dynamics of optical solitons for nonlinear directional couplers. This coupler system is considered with the group velocity dispersion and the cross-phase modulation of two components along with the spatiotemporal dispersion coefficients. The constraint conditions for the existence of optical Gaussons and dark solitons are listed under the log law and Kerr law nonlinearities, repectively. Additionally, a couple of other solutions known as singular periodic and combined dark-singular solitons, fall out as a by-product of this scheme. This scheme however fails to retrieve bright soliton solution.

(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.

New optical solitons of cubic-quartic nonlinear Schrödinger equation

The present paper acquires new optical solitons to the nonlinear Schrödinger equation (NLSE) which is investigated with third and fourth order dispersion terms. A modified form of Kudryashov approach is formally adopted to extract the exact analytical solutions of governing model. The constraint conditions for the existence of optical solitons in the case of Kerr law nonlinearity are also reported.

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.

Dispersive optical solitons and modulation instability analysis of Schrödinger-Hirota equation with spatio-temporal dispersion and Kerr law nonlinearity

This paper obtains the dark, bright, dark-bright or combined optical and singular solitons to the perturbed nonlinear Schrödinger-Hirota equation (SHE) with spatio-temporal dispersion (STD) and Kerr law nonlinearity in optical fibers. The integration algorithm is the Sine-Gordon equation method (SGEM). Furthermore, the modulation instability analysis (MI) of the equation is studied based on the standard linear-stability analysis and the MI gain spectrum is got.

Dark optical solitons and conservation laws to the resonance nonlinear Shrödinger's equation with Kerr law nonlinearity

In this work, we investigate the soliton solutions to the resonant nonlinear Shrödinger's equation (R-NSE) with Kerr law nonlinearity. By adopting the Riccati–Bernoulli sub-ODE technique, we present the exact dark optical, dark-singular and periodic singular soliton solutions to the model. The soliton solutions appear with all necessary constraint conditions that are necessary for them to exist. We studied the R-NSE by analyzing a system of nonlinear partial differential equations (NPDEs) obtained by decomposing the equation into real and imaginary components. We derive the Lie point symmetry generators of the system, then we apply the general conservation theorem to establish a set of nontrivial and nonlocal conservation laws (Cls). Some interesting figures for the acquired solutions are Cls also presented.

Cubic–quartic optical solitons in Kerr and power law media

In this paper, we present the exact bright and singular optical solitons of the nonlinear Schrödinger equation with third and fourth order dispersion terms. The method of undetermined coefficients is applied to obtain the reported solutions. The cases of Kerr law and power law nonlinearity are taken into account. We also find the conditions concerning the optical material parameters for the existence of these soliton structures. The results are useful in describing the propagation of optical solitons in highly dispersive media with Kerr and power law nonlinearity.

Parallel propagation of dispersive optical solitons by extended trial equation method

This paper applied extended trial equation algorithm to obtain dispersive optical solitons in DWDM system that is governed by the Schrödinger–Hirota equation with Kerr law nonlinearity. Bright and singular soliton solutions are reported.

The Dynamics of Thirring Optical Solitons by Kerr Law Nonlinearity

Bu makalede Thirring optikal solitonlarin dinamigi calisildi. Tam cozumler icin Jacobi eliptik fonksiyonlar dusunuldu ve lineer olmayanlik Kerr law ile tanimlandi. Sonucta, Dark ve Bright optikal solitonlar ile tekil cozumler elde edildi

Kerr-law nonlinearity of the resonant nonlinear Schrodinger’s equation with time-dependent coefficients

This work deals with exact soliton solutions of the resonant nonlinear Schrodinger equation with time-dependent coefficients. The propagation equation that is the resonant dispersive nonlinear Schrodinger’s equation with Kerr law nonlinearity is studied by two analytical methods, namely, the improved tan( $$\phi /2$$ )-expansion method (ITEM) and He’s semi-inverse variational method (HSIVM), based upon the integration tools. 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 the HSIVM we obtained the bright soliton wave solution. Finally, by using Matlab, some graphical simulations were done to see the behavior of these solutions.