Presence Of Perturbation Terms Research Articles

Bifurcation Analysis and Chaotic Behavior of the Concatenation Model with Power-Law Nonlinearity

This paper presents a comprehensive analysis of the concatenation model with power-law nonlinearity. The research encompasses multiple key aspects, providing a detailed exploration of the model's behavior and implications within the context of nonlinear dynamics and optics. The study commences with an in-depth bifurcation analysis, aiming to unravel the intricate dynamics and transitions within the system. This analysis not only uncovers the system's behavior under varying conditions but also sheds light on its stability and the emergence of bifurcation phenomena. Our research delves into the retrieval of soliton solutions within the model. The exploration of solitons is of paramount significance, offering insights into localized, self-sustaining waveforms that often play a crucial role in nonlinear systems. These soliton solutions are identified, characterized, and their relevance to the model is established. The paper addresses the complex dynamics of the system in the presence of perturbation terms. By incorporating perturbations into the analysis, we elucidate how external influences impact the system's behavior and lead to chaotic phenomena. This analysis helps uncover the system's sensitivity to external factors and provides a deeper understanding of chaotic behavior.

Sequel to “Quasi-monochromatic dynamical system of cubic–quartic optical solitons with Kerr law of nonlinear refractive index” (Power law)

This paper presents the adiabatic dynamical system of cubic–quartic soliton conserved quantities in presence of perturbation terms. The considered nonlinearity is with power law. The slow velocity change is also computed and exhibited.

Quasi-monochromatic dynamical system of cubic–quartic optical solitons with Kerr law of nonlinear refractive index

This paper displays the quasi-monochromatic dynamical system of the cubic–quartic soliton parameters that are recovered from the conservation laws of the model. The adiabatic change in soliton velocity in presence of perturbation terms is also presented.

Cubic–quartic nonlinear Schrödinger equation in birefringent fibers with the presence of perturbation terms

ABSTRACT In this paper, we derive the solitons solutions to the cubic–quartic nonlinear Schrödinger equation (CQ-NLSE) in birefringent fibers with three laws of nonlinearity. These laws are parabolic law, quadratic-cubic law and non-local law. The new extended generalized Kudryashov method and our new method proposed for the first time have been applied. Many solutions have been found. Dark, bright and singular soliton solutions existed under constraint conditions. The comparative analysis of the two proposed methods shows that in the two cases of parabolic and non-local laws, the first method gives the dark and singular solitons in terms of tanh–coth hyperbolic functions, respectively, while the second method gives the bright and singular solitons in terms of sech–csch hyperbolic functions, respectively. But in the case of quadratic-cubic law, both methods give the bright-singular solitons in terms of sech–csch hyperbolic functions, respectively, with different arguments.

Chirped optical soliton perturbation of Fokas\u2013Lenells equation with full nonlinearity

The present paper focuses on the chirped soliton solutions of the Fokas–Lenells equation in the presence of perturbation terms. A complex envelope traveling-wave solution is used to reduce the governing equation to an ordinary differential equation (ODE). An auxiliary equation in the form of a first-order nonlinear ODE with six-degree terms is implemented as a solution method. Various types of chirped soliton solutions including bright, dark, kink and singular solitons are extracted. The associated chirp is also determined for each of these optical pulses. Restrictions for the validity of chirped soliton solutions are presented.

Optical solitary wave and elliptic function solutions of the Fokas–Lenells equation in the presence of perturbation terms and its modulation instability

In this paper, we study the Fokas–Lenells (F-L) equation in the presence of perturbation terms and we construct exact solutions. The modified extended direct algebraic method (MEDAM) is utilized, and soliton solutions, solitary wave solutions and elliptic function solutions are achieved. The physical meaning of the geometrical shapes for some of the obtained results is investigated for various choices of the free parameters that appear in the results. The stability of the model is investigated by using the standard linear stability analysis, which verifies that the exact solutions are stable. The achieved solutions and computational work show that the current method is powerful and influential.

Chirped optical Gausson perturbation with quadratic–cubic nonlinearity by collective variables

Here, collective variables approach is applied to obtain optical solitons in the presence of perturbation terms. Gaussian solitons are selected to retain the pulse to establish soliton setting. The numerical simulations of soliton parameters are performed for specific values of the Gaussian pulse parameters.

Abundant complex wave solutions for the nonautonomous Fokas–Lenells equation in presence of perturbation terms

This paper mainly investigates the nonautonomous Fokas–Lenells equation (FLE) in presence of perturbation terms. Bright–dark soliton solutions, Arbitrary solutions, similarity solutions, and some exact solutions for the FLE are obtained by different techniques. Furthermore, some figures are given to explain the movement mechanism of these solutions. To our best knowledge, the discussion and results in this work are new and important in different branches of science where this equation is used to describe some physical phenomenon.

New optical solitary wave solutions of Fokas-Lenells equation in presence of perturbation terms by a novel approach

A variety of new optical waves solutions of the Fokas-Lenells equation in presence of perturbation terms is investigated. A new approach is used, namely the generalized exponential function method. The physical meaning of the geometrical structures for some of these solutions is discussed for different choices of the free parameters present in the solutions. It is shown that the proposed methodology provides powerful mathematical tools for obtaining the exact traveling wave solutions of different nonlinear evolution equations.

Optical soliton perturbation in magneto-optic waveguides

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.

Resonant optical solitons with anti-cubic nonlinearity

This work obtains the integration of the resonant nonlinear Schrödinger's equation, with anti-cubic nonlinearity, in presence of perturbation terms that are considered with full nonlinearity. The csch method, extended tanh–coth method and the modified simple equation method are applied to extract the analytical soliton solution.

Optical solitons in birefringent fibers with modified simple equation method

This paper applied modified simple equation method to extract soliton solutions to birefringent fibers, in presence of perturbation terms. Both Kerr law and parabolic law of nonlinearity are studied. Dark and singular optical soliton solutions are listed for these nonlinearities. The existence of these solitons is guaranteed with appropriate constraints that are also presented.

Dispersive optical solitons with Schrödinger–Hirota equation

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.

Perturbation of shallow water waves by semi-inverse variational principle

This paper addresses the shallow water waves along with its perturbation terms that are modeled by Boussinesq equation. The power law nonlinearity is taken into consideration for a generalized setting. The semi-inverse variational principle is employed to derive the soliton solution in presence of perturbation terms. A couple of numerical simulations illustrate the analytical development.

Quasi-stationary optical Gaussons

This paper studies the dynamics of optical solitons with log law nonlinearity, also known as optical Gaussons, in the presence of perturbation terms. The multiple-scale perturbation analysis is applied to obtain the quasi-stationary optical Gaussons solution. The definition of the phase that is introduced in this paper reveals a couple of resonant conditions that cannot be otherwise recovered. A numerical simulation is also included.

Adiabatic phase variation for optical Gaussons

This paper studies the adiabatic phase variation of optical Gaussons in the presence of perturbation terms. The modified conservation law of phase variation is used to carry out this analysis.

QUASI-STATIONARY OPTICAL SOLITONS IN NON-KERR LAW MEDIA WITH FULL NONLINEARITY

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.

Optical soliton perturbation in non-Kerr law media: Traveling wave solution

This paper analyses the dynamics of soliton propagation through optical fibers with non-Kerr law nonlinearities. The governing nonlinear Schrödinger equation is integrated in the presence of perturbation terms. The traveling wave hypothesis is used to carry out the integration. Domain restrictions on the soliton parameters are identified in the process. The five forms of nonlinearity that are studied are Kerr-law, power-law, parabolic-law, dual-power law and the log-law nonlinearity. Numerical simulations are presented for each of these nonlinear media.

Perturbation of dispersive topological solitons

This paper studies the dynamics of topological solitons in the cases of the dispersive sine-Gordon equation, the double sine-Gordon equation and the triple sine-Gordon equation. The adiabatic dynamics of the soliton velocity are also obtained for each case in the presence of perturbation terms.

A study of solitary waves by He's semi-inverse variational principle

The dynamics of solitary waves in the presence of perturbation terms is studied in this paper with the aid of the semi-inverse variational principle. In this paper, shallow water waves as well as internal gravity waves in a density-stratified ocean are considered. These are respectively modeled by the Korteweg–de Vries equation as well as the compound Korteweg–de Vries equation. An analytical solution of the solitary wave is found in each case.