Nonlinear Chromatic Dispersion Research Articles

Revisitation of “Implicit Quiescent Optical Solitons with Complex Ginzburg-Landau Equation Having Nonlinear Chromatic Dispersion“: Linear Temporal Evolution

The current paper revisits the retrieval of quiescent optical solitons for the complex Ginzburg-Landau equation with nonlinear chromatic dispersion and several forms of self-phase modulation. The results obtained in this work consist of explicit or implicit quiescent optical solitons, unlike the previous report, which were expressed in terms of quadratures. Additionally, this study addresses two additional forms of self-phase modulation: the saturating law and the exponential law. This exploration yields quiescent optical solitons expressed in terms of quadratures for the first time.

Revisitation of “implicit quiescent optical solitons with complex Ginzburg–Landau equation having nonlinear chromatic dispersion": generalized temporal evolution

AbstractThis paper is a revisitation to the study on the retrieval of quiescent optical solitons to the complex Ginzburg–Landau equation that is considered with generalized temporal evolution and nonlinear chromatic dispersion. The results are recovered with the application of Lie symmetry. Apart from a couple of self-phase modulation structures where the results are in quadratures, the integrals are with a range of special functions. Two new forms of self-phase modulation structures are addressed in the paper.

Optical solitons and stability analysis for NLSE with nonlocal nonlinearity, nonlinear chromatic dispersion and Kudryashov’s generalized quintuple-power nonlinearity

In this paper, we consider the nonlinear Schrödinger equation (NLSE) with nonlocal nonlinearity having nonlinear chromatic dispersion and Kudryashov’s generalized quintuple-power. For the suggested model, dark solitons, and singular solitons are investigated using the modified extended mapping approach. Furthermore, rational solutions, exponential solutions, hyperbolic wave solutions, singular periodic solutions, and Jacobi elliptic function solutions are shown. We impose certain limits on the parameters in order to guarantee the existence of the obtained soliton solutions. Furthermore, a few chosen solutions are also displayed graphically to illustrate the physical characteristics of the precise solutions. Furthermore, we use the idea of modulation instability analysis to discuss the stability of the derived wave solutions.

Implicit quiescent optical solitons For Lakshmanan–Porsezian–Daniel model having nonlinear chromatic dispersion and power-law of self-phase modulation by lie symmetry

AbstractThis paper recovers implicit quiescent optical solitons for the Lakshmanan–Porsezian–Daniel equation that is studied with nonlinear chromatic dispersion and power-law of self-phase modulation. The Lie symmetry analysis has made this retrieval possible. An interesting observation has been made with the results that was not recoverable from the prequel paper.

Quiescent Bright Optical Solitons for Radhakrishnan�Kundu�Lakshmanan Equation with Nonlinear Chromatic Dispersion and Power�Law of Self�Phase Modulation by Lie Symmetry

Quiescent Bright Optical Solitons for Radhakrishnan�Kundu�Lakshmanan Equation with Nonlinear Chromatic Dispersion and Power�Law of Self�Phase Modulation by Lie Symmetry

Quiescent Optical Solitons for Fokas�Lenells Equation with Nonlinear Chromatic Dispersion Having Quadratic and Quadratic-Quartic Forms of Self-Phase Modulation

Quiescent Optical Solitons for Fokas�Lenells Equation with Nonlinear Chromatic Dispersion Having Quadratic and Quadratic-Quartic Forms of Self-Phase Modulation

Implicit quiescent optical solitons for the concatenation model with nonlinear chromatic dispersion and in absence of self-phase modulation by lie symmetry

Implicit quiescent optical solitons for the concatenation model with nonlinear chromatic dispersion and in absence of self-phase modulation by lie symmetry

Implicit quiescent optical solitons for the concatenation model with Kerr law nonlinearity and nonlinear chromatic dispersion by Lie symmetry

Implicit quiescent optical solitons for the concatenation model with Kerr law nonlinearity and nonlinear chromatic dispersion by Lie symmetry

Quiescent Optical Solitons for the Concatenation Model Having Nonlinear Chromatic Dispersion with Differential Group Delay

This study recovers quiescent optical solitons within a complex concatenation model featuring nonlinear chromatic dispersion and differential group delay. It employs the sine-Gordon equation approach and the projective Riccati equation scheme. The results include the successful recovery of soliton solutions and the identification of parameter restrictions for their existence. The novelty lies in the application of these methods to this specific problem, offering valuable insights for optical communication system design.

Implicit quiescent optical solitons for the concatenation model with nonlinear chromatic dispersion and power–law of self–phase modulation by Lie symmetry

Implicit quiescent optical solitons for the concatenation model with nonlinear chromatic dispersion and power–law of self–phase modulation by Lie symmetry

Implicit Quiescent Optical Solitons for the Dispersive Concatenation Model with Nonlinear Chromatic Dispersion by Lie Symmetry

The primary purpose of this paper is to investigate and recover implicit quiescent optical solitons in the context of the dispersive concatenation model in nonlinear optics. Specifically, the study focuses on a model that incorporates nonlinear chromatic dispersion and includes Kerr and power-law self-phase modulation effects. The objective is to identify and characterize these soliton solutions within this complex optical system. To achieve this purpose, we employ the Lie symmetry analysis method. Lie symmetry analysis is a powerful mathematical technique commonly used in physics and engineering to identify symmetries and invariance properties of differential equations. In this context, it is used to uncover the underlying symmetries of the nonlinear optical model, which in turn aids in the recovery of the quiescent optical solitons. This method involves mathematical derivations and calculations to determine the solutions. The outcomes of the current paper include the successful recovery of implicit quiescent optical solitons for the dispersive concatenation model with nonlinear chromatic dispersion, Kerr, and power-law self-phase modulation. The study provides mathematical expressions and constraints on the model’s parameters that yield upper and lower bounds for these solutions. Essentially, this paper presents a set of mathematical descriptions for the optical solitons that can exist within the described optical system. The present paper contributes to the field of nonlinear optics by exploring the behavior of optical solitons in a model that combines multiple nonlinear effects. This extends our understanding of complex optical systems.

Chirped optical solitons and stability analysis of the nonlinear Schrödinger equation with nonlinear chromatic dispersion

The present paper aims to investigate the chirped optical soliton solutions of the nonlinear Schrödinger equation with nonlinear chromatic dispersion and quadratic-cubic law of refractive index. The exquisite balance between the chromatic dispersion and the nonlinearity associated with the refractive index of a fiber gives rise to optical solitons, which can travel down the fiber for intercontinental distances. The effective technique, namely, the new extended auxiliary equation method is implemented as a solution method. Different types of chirped soliton solutions including dark, bright, singular and periodic soliton solutions are extracted from the Jacobi elliptic function solutions when the modulus of the Jacobi elliptic function approaches to one or zero. These obtained chirped optical soliton solutions might play an important role in optical communication links and optical signal processing systems. The stability of the system is examined in the framework of modulational instability analysis.

Qualitative analysis and stationary optical patterns of nonlinear Schrödinger equation including nonlinear chromatic dispersion

Qualitative analysis and stationary optical patterns of nonlinear Schrödinger equation including nonlinear chromatic dispersion

Quiescent Optical Solitons for the Concatenation Model with Nonlinear Chromatic Dispersion

This paper recovers quiescent optical solitons that are self-sustaining, localized wave packets that maintain their shape and amplitude over long distances due to a balance between nonlinearity and dispersion. When a soliton is in a state of quiescence, it means that it is stationary in both space and time. Quiescent optical solitons are typically observed in optical fibers, where nonlinearity and dispersion can lead to the formation of solitons. The concatenation model is considered to understand the behavior of optical pulses propagating through nonlinear media. Here, we consider the familiar nonlinear Schrödinger equation, the Lakshmanan–Porsezian–Daniel equation, and the Sasa–Satsuma equation. The current paper also addresses the model with nonlinear chromatic dispersion, a phenomenon that occurs in optical fibers and other dispersive media, where the chromatic dispersion of the material is modified by nonlinear effects. In the presence of nonlinearities, such as self-phase modulation and cross-phase modulation, the chromatic dispersion coefficient becomes a function of the optical intensity, resulting in nonlinear chromatic dispersion. A full spectrum of stationary optical solitons, along with straddled stationary solitons, are obtained. There are four integration schemes that made this retrieval possible. The numerical simulations are also included for these solitons. The parameter constraints also indicate the existence criteria for these quiescent solitons.

Bifurcation analysis, stationary optical solitons and exact solutions for generalized nonlinear Schrödinger equation with nonlinear chromatic dispersion and quintuple power-law of refractive index in optical fibers

In this paper, the bifurcation, stationary optical solitons and exact solutions in optical fiber propagation are studied. The propagation model is described by a generalized nonlinear Schrödinger equation with Kudryashov’s quintuple power law of refractive index. First, the equation is transformed into a second-order nonlinear ordinary differential equation by an appropriate transformation. Then, the bifurcation of the phase diagram of the obtained ordinary differential equation is established using planar dynamic system theory, and the types of optical solitons and exact solutions are determined. What is more, the stationary optical solitons and exact solutions are obtained by the polynomial complete discriminant system, and are demonstrated in 3D and 2D graphics by using the symbolic computation software Maple. Finally, the obtained stationary optical solitons and exact solutions include the Jacobi elliptic function solution, hyperbolic function solution, rational function solution, trigonometric function solution and exponential function solution. Moreover, the results provide a method to further study stationary optical solitons and exact solutions of propagation pulses in optical fibers.

Quiescent Optical Solitons with Quadratic-Cubic and Generalized Quadratic-Cubic Nonlinearities

This paper studies the formulation of dark and singular stationary optical solitons that stem from quadratic-cubic and generalized quadratic-cubic forms of nonlinear refractive index coupled with nonlinear chromatic dispersion. The temporal evolution is taken to be of both kinds, namely linear and generalized. The enhanced Kudryashov’s approach enables this retrieval possible.

Quiescent optical solitons with Kudryashov's generalized quintuple-power and nonlocal nonlinearity having nonlinear chromatic dispersion: generalized temporal evolution

Quiescent optical solitons with Kudryashov's generalized quintuple-power and nonlocal nonlinearity having nonlinear chromatic dispersion: generalized temporal evolution

Bifurcations, stationary optical solitons and exact solutions for complex Ginzburg–Landau equation with nonlinear chromatic dispersion in non-Kerr law media

Bifurcations, stationary optical solitons and exact solutions for complex Ginzburg–Landau equation with nonlinear chromatic dispersion in non-Kerr law media

Quiescent Optical Solitons with Kudryashov’s Generalized Quintuple-Power and Nonlocal Nonlinearity Having Nonlinear Chromatic Dispersion

The paper derives stationary optical solitons with nonlinear chromatic dispersion. A nonlocal form of nonlinearity and quintuple power–law of nonlinearity are considered. The Kudryashov’s integration scheme enables to retrieve such solitons. A plethora of solitons come with this algorithm.

Dynamical behavior of solitons with Kudryashov’s quintuple power-law of refractive index having nonlinear chromatic dispersion using improved modified extended tanh-function method

In this article, the improved modified extended tanh-function method is applied for nonlinear Schrödinger equation with Kudryashov’s quintuple power-law of refractive index having nonlinear chromatic dispersion. Various types of solutions are extracted such as bright soliton solutions, dark soliton solutions, singular soliton solutions, periodic solutions, singular periodic solutions, rational solutions, exponential type solutions, hyperbolic type solutions and Weierstrass elliptic doubly periodic type solutions. Moreover, for the physical illustration, some of the obtained solutions are represented graphically.