Inhomogeneous Optical Fiber Research Articles

Localized wave solutions to coupled variable-coefficient fourth-order nonlinear Schrödinger equations

This study investigates higher-order localized waves for coupled variable-coefficient fourth-order nonlinear Schrödinger equations, which are used to describe the simultaneous propagation of optical pulses in an inhomogeneous optical fiber. Based on the seed solutions and Lax pair, the Nth-order localized wave solutions are constructed. The interactions of rogue waves with dark–bright solitons are graphically analyzed via numerical simulation. The results are helpful for studying localized wave phenomena in nonlinear optics.

Controlled linearly chirped similaritons in inhomogeneous birefringent optical fibers

By similarity transformation, optical similaritons in a nonlinear birefringent optical fiber are investigated within the framework of two coupled nonlinear Schrödinger equations with space-modulated self- and cross-phase modulation nonlinearities, group velocity dispersion, external electro-optic phase modulation, and gain/loss. We find that the birefringent nonlinear medium with spatial parameter variations supports the existence of linearly chirped similariton structures of the W-shaped-dipole and bright-dipole types. These important results indicate that in addition to the usual single-humped localized waves such as bright-bright and dark-dark type waveforms, multihump chirped similaritons can also exist in the inhomogeneous birefringent fiber in the presence of all physical effects. The similariton parameters such as the amplitude, width, phase, and inverse group velocity are found to be dependent on certain controllable fiber parameters, thus enabling us to manage their intensity and consequently their subsequent dynamical evolution. Finally, we investigate the transmission of similaritons for different choices of material parameters.

Superposition of modulated nonlinear waves in inhomogeneous systems with negative coherent coupling

The superimposed wave solutions of the variable coefficient nonlinear Schrödinger equations with negative coherent coupling are derived under a more relaxed constraint condition than those in previous literatures. For the benefit of the more relaxed constraint, the dispersion, nonlinearity, and gain/loss can be designed freely, and the obtained solutions can describe the nonlinear waves in general inhomogeneous optical fiber systems. The obtained solutions with two free phase parameters can be deemed to be the superposition of the typical simple modulated solutions, and the arbitrary of the optical parameters and the free phase parameters be expected to give the rise of abundant forms of modulation functions, that leads to the diverse characteristics of superimposed waves. Take the kink dispersion fiber systems with constant gain/loss and trigonometric gain/loss as examples, rich dynamics of the superimposed waves are displayed. By changing the gain/loss, the physical features of superimposed waves, such as the amplitudes of solitons and Kuznetsov-Ma breathers, the widths of solitons, the distances between Kuznetsov-Ma breathers, and the backgrounds of Akhmediev breathers and rogue waves can be controlled. The interaction of solitons or Kuznetsov-Ma breathers, and the number of the rogue waves or Akhmediev breathers can also be manipulated by selecting appropriate value of gain/loss. The results presented here may be useful to explore the diverse dynamics of superimposed waves and prove significance for the control of nonlinear waves in weakly birefringent fibers.

Discrete solutions and interaction dynamics for coupled nonlocal discrete nonlinear Schrödinger equations in an inhomogeneous optical fiber

The nonlinear Schrödinger (NLS) equation has made great achievement, however the coupled nonlocal discrete nonlinear Schrödinger (CNDNLS) equations have less works. In this paper, we investigate the Darboux transformation (DT) method to obtain discrete soliton solutions of CNDNLS equations. We present two different kinds of solutions through choosing different seed solutions, and analysis the relations among them. Further many novel discrete 1-soliton and 2-soliton are derived with the zero and nonzero seed solutions. Meanwhile, the elastic interaction dynamic of two discrete solitons is displayed, it is shown that the amplitudes keep unchanged after the interactions in long time.

Multi-soliton solutions and asymptotic analysis for the coupled variable-coefficient Lakshmanan-Porsezian-Daniel equations via Riemann-Hilbert approach

In this paper, we study multi-soliton solutions and asymptotic analysis for the coupled variable-coefficient Lakshmanan-Porsezian-Daniel equations, which describe the simultaneous propagation of nonlinear waves in the inhomogeneous optical fibers. We analyze the spectrum of the Lax pair to establish the Riemann-Hilbert problem. Using such Riemann-Hilbert problem, we calculate various multi-soliton solutions without reflection, including breather-like and mixed solitons. We illustrate the propagation and interaction dynamics of the solitons through appropriate parameter selection and asymptotic analysis. We find that the interaction between solitons is elastic, the amplitudes of solitons are only determined by the initial velocity and interaction, and the soliton with lower energy always yields a position shift when elastic interaction occurs. In addition, we observe that the existence time of the wave changes with energy and that multiple elastic interactions between solitons can be obtained when we choose appropriate variable coefficients. Then, we investigate the influences of group velocity dispersions and fourth-order dispersions on the interactions of solitons through parameter modulation mode and asymptotic analysis. Furthermore, we present several new types of nonlinear phenomena graphically, including elastic interactions between parabolic solitons and hump-type solitons, elastic interactions between cubic solitons and hump-type solitons, and periodic-changing propagations.

Generalized Darboux transformation and rogue waves for a coupled variable-coefficient nonlinear Schrödinger system in an inhomogeneous optical fiber

Generalized Darboux transformation and rogue waves for a coupled variable-coefficient nonlinear Schrödinger system in an inhomogeneous optical fiber

On complex wave solutions for the variable-coefficient fourth-order nonlinear Schrödinger system in an inhomogeneous optical fiber

In this paper, the variable-coefficient fourth-order nonlinear Schrödinger system, which is used to depict the simultaneous propagation of ultrashort optical pulses in an inhomogeneous optical fiber, is probed by two approaches. As an achievement, heaps of complex exact solutions, including some complex solitary, soliton and elliptic wave solutions as well as some complex trigonometric, hyperbolic trigonometric and rational solutions, are derived in the light of the unified and improved F-expansion methods separately. Additionally, the movement mechanisms of partial solutions that we gain are graphically discussed with appropriate parameters. And one thing should be mentioned is that we choose one solution from every foregoing category of solutions to draw the 2D, 3D and contour images to realize the wave propagation more systematically and deeply.

Conservation laws, [formula omitted]-fold Darboux transformation, [formula omitted]-dark-bright solitons and the [formula omitted]th-order breathers of a variable-coefficient fourth-order nonlinear Schrödinger system in an inhomogeneous optical fiber

Optical fiber communication system is one of the core supporting systems of the modern internet age. For the simultaneous propagation of nonlinear waves in an inhomogeneous optical fiber, in this work, a coupled variable-coefficient fourth-order nonlinear Schrödinger system is studied. Infinitely-many conservation laws and N-fold Darboux transformation (DT) based on the existing Lax pair under certain constraints are derived, where N is a positive integer. Via the N-fold DT, the N-dark-bright soliton and Nth-order breather solutions under certain constraints are given. Interactions between the two dark-bright solitons are depicted graphically when the dispersion coefficient in that system, γ1(t), and the group velocity dispersion coefficient in that system, σ(t), are the constants and periodic functions, where t means the normalized retarded time. It is found that the velocities of the two dark-bright solitons increase as γ1(t) and σ(t) increase when γ1(t) and σ(t) are the constants. Interactions between the two breathers are presented graphically.

Jacobian-elliptic-function and rogue-periodic-wave solutions of a high-order nonlinear Schrödinger equation in an inhomogeneous optical fiber

Optical fiber communication plays an important role in the modern communication. Under investigation is a high-order nonlinear Schrödinger equation with the additional high-order dispersion and nonlinear terms in an inhomogeneous optical fiber. We give the Jacobian-elliptic-function solutions of that equation. Based on the nonlinearization of the existing Lax pair, we obtain the values of the spectral parameters corresponding to that Lax pair. We construct the linearly-independent and non-periodic solutions of that Lax pair. We take the Jacobian-elliptic-function solutions as the seed solutions, and substitute the linearly-independent and non-periodic solutions into the Darboux transformation to obtain the rogue-periodic-wave solutions. For the one-fold rogue-dn-periodic wave, when the parameter γ of the equation increases, we find that the period and maximum amplitude of the one-fold rogue-dn-periodic wave remain unchanged, while the minimum amplitude decreases. When the parameter η of the equation increases, we find that the maximum amplitude of the one-fold rogue-dn-periodic wave remains unchanged, while the period becomes the smaller. For the one-fold rogue-cn-periodic wave, the same conclusions can be observed. For the two-fold rogue-cn-periodic wave, when the parameter γ of the equation increases, we find that the period and maximum amplitude of the two-fold rogue-cn-periodic wave remain unchanged, while the minimum amplitude rises. When the parameter η of the equation increases, we find that the maximum amplitude of the two-fold rogue-cn-periodic wave remains unchanged, while the period becomes the smaller.

Localized wave solutions to a variable-coefficient coupled Hirota equation in inhomogeneous optical fiber

The first- and second-order localized waves for a variable-coefficient coupled Hirota equation describe the vector optical pulses in inhomogeneous optical fiber and are investigated via generalized Darboux transformation in this work. Based on the equation’s Lax pair and seed solutions, the localized wave solutions are calculated, and the dynamics of the obtained localized waves are shown and analyzed through numerical simulation. A series of novel dynamical evolution plots illustrating the interaction between the rogue waves and dark-bright solitons or breathers are provided. It is found that functions have an influence on the propagation of shape, period, and velocity of the localized waves. The presented results contribute to enriching the dynamics of localized waves in inhomogeneous optical fiber.

Nonautonomous three soliton interactions in an inhomogeneous optical fiber: Application to soliton switching devices

We investigate the interactional behavior of three nonautonomous solitons in an optical fiber with inhomogeneous nature which can be described by nonlinear Schrödinger equation with nonautonomous term. A pair of matrices constructed with the aid of AKNS procedure for nonautonomous NLS equation with variable coefficients. Based on the Lax pair, three soliton solutions are generated by employing Darboux method. We show the switchable characteristics of nonautonomous three solitons by typical graphical illustration. The remarkable results presented in this study can be used to design the optical logic gate devices for optical computing.

Chirped self-similar localized pulses on a continuous wave background in presence of cubic–quintic nonlinearity and self-frequency shift

We investigate the nonlinear pulse propagation through an inhomogeneous single-mode optical fiber where the evolution dynamics is governed by the generalized higher-order nonlinear Schrödinger equation with varying group velocity dispersion, cubic and quintic nonlinearities, self-frequency shift arising from stimulated Raman scattering, and linear gain or loss. A new class of soliton pulse solutions for a wave field is constructed based on the similarity transformation connecting with the constant-coefficient Kundu–Eckhaus equation. This class describes soliton structures that propagate self-similarity on a continuous-wave (cw) background, and acquires a nonlinear chirp as it propagates in the inhomogeneous fiber medium. It is found that the nonlinear chirp associated with these self-similar pulses originates essentially from the self-frequency shift effect. The conditions on fiber parameters for the existence of those nonlinearly chirped self-similar localized pulses are also given. As a practical example, we studied their evolution dynamics in a specified soliton control system. The solution stability against perturbation is checked by direct numerical simulation.

Study on the regulation of amplitude for the optical soliton through nonlinear effects in the optical communication system

Optical communication system is a kind of communication system using the light wave as the carrier. It has been widely used in recent years with the advantages of the long distance. Optical solitons have some merits for high stability, amenable to generate and low cost, it is an ideal carrier of optical communication system. In this paper, the regulation of pulse characteristics of the optical soliton is studied theoretically. The influence of high-order dispersion and high-order nonlinear effects on the amplitude, shape and other transmission characteristics of the optical soliton is studied by using the bilinear method with the high-order variable coefficient nonlinear Schrödinger (NLS) equation in the nonuniform fibers, and the regulation problems such as the maintenance and excitation of the optical soliton are analyzed. The waveform and amplitude control of the optical soliton and the change of optical soliton characteristics with the dispersion management are studied profoundly, and the nonlinear dynamic processes in their respective intracavity are analyzed. A feasible scheme for avoiding and utilizing the optical soliton is proposed, which has the significance for the investigation of the parameter regulation and dynamic control of the optical soliton in practical inhomogeneous optical fiber communication systems.

Dark soliton solutions for the coupled variable-coefficient fourth-order nonlinear Schrödinger equations in the inhomogeneous optical fiber

In this paper, we discuss the bright–dark and dark–dark soliton solutions for the coupled variable-coefficient fourth-order nonlinear Schrödinger equations, which describe the nonlinear waves propagating simultaneously in an inhomogeneous optical fiber. The bilinear forms with auxiliary functions are derived through the Hirota method. Based on the bilinear forms, we construct the bright–dark and dark–dark soliton solutions. The effects of variable coefficients on structures of the bright–dark and dark–dark solitons are analyzed. The propagation of bright–dark soliton and elastic interactions between dark–dark multi-solitons are illustrated graphically.

The exact solutions for the nonlinear variable-coefficient fifth-order Schrödinger equation

In the paper, the nonlinear variable-coefficient fifth-order Schrödinger (NLVS) equation is researched. The NLVS equation is an integrable equation, which can be described the spreading of ultrashort pulses in an inhomogeneous optical fiber. Firstly, by using the modified traveling wave transformation, the NLVS equation is changed into an ordinary equation. Secondly, by the Jacobian elliptic function expansion method for the ordinary equation, we obtain the exact solutions for the ordinary equation, and then, we obtain the exact solutions to the NLVS equation. These solutions mainly include three types: Jacobi elliptic function solutions, hyperbolic function solutions, and triangular function solutions. Finally, according to the special parameters, we show the figures of the exact solutions.

Darboux transformation, localized waves and conservation laws for an [formula omitted]-coupled variable-coefficient nonlinear Schrödinger system in an inhomogeneous optical fiber

Optical fiber communication system is one of the supporting systems in the modern internet age. We investigate an M-coupled variable-coefficient nonlinear Schrödinger system, which describes the simultaneous pulse propagation of the M-field components in an inhomogeneous optical fiber, where M is a positive integer. With respect to the complex amplitude of the jth-field (j=1,…,M) component in the optical fiber, we construct an n-fold Darboux transformation, where n is a positive integer. Based on the n-fold Darboux transformation, we obtain some one- and two-fold localized wave solutions for the above system with the mixed defocusing-focusing-type nonlinearity and M=2. We acquire the infinitely-many conservation laws. Via such solutions, we obtain some vector gray solitons, interactions between the two vector parabolic/cubic gray solitons, and interactions between the vector parabolic/cubic breathers and gray solitons with different β(z), γ(z) and δ(z), the coefficients of the group velocity dispersion, nonlinearity and amplification/absorption. It can be found that δ(z) affects the backgrounds of the breathers and gray solitons.

Periodic and nonperiodic amplifications of attosecond solitons in an inhomogeneous lossy optical fiber

We investigate the variable-coefficient generalized higher order nonlinear Schrödinger equation which governing the attosecond optical soliton propagation in an inhomogeneous fiber system. Three-soliton solutions are attained through Darboux transformation based on the Lax pair. Using three soliton solutions, we investigate the periodic and nonperiodic amplification of three solitons by adopting certain functions to variable coefficients. Various amplification schemes are demonstrated graphically via symbolic computation. Especially, periodic and nonperiodic amplifications are attained under dispersion and nonlinearity management. In order to realize the soliton amplifications, two different set of variable coefficients profiles are employed. The results obtained in this work will be helpful for designing the optical amplification devices by soliton control technology.

Formula omitted]th-order rogue wave solutions for a variable coefficient Schrödinger equation in inhomogeneous optical fibers

In investigation is a nonlinear Schrödinger equation with variable coefficients, which can describe pulse propagation in inhomogeneous optical fiber systems. The variable coefficients can used to control the dispersion and nonlinearity factors. Through extending Darboux transformation iteration algorithm, analytical Nth-order rogue wave solutions are obtained for the equation. Based on the two free variable coefficient function involved in the solutions, novel rogue waves can be excited by choosing them as specific functions. Polynomial and periodic functions are taken as examples to how to excite rich rogue wave solutions. The results show that as the orders of the rogue wave solutions increase, the spatio-temporal patterns become more complex, while the amplitudes also increase rapidly. These properties will play critical roles in high-capacity information transmission and signal amplification in optical systems.

Boomerons in a three-coupled NLS system with inhomogeneous dispersion and nonlinearity

This study investigates the dynamics of boomerang solitons and their interactions in three-mode fiber under the influence of inhomogeneous effects governed by three-coupled nonlinear Schrödinger (3-CNLS) equations in GVD and nonlinearity coefficients. Also, 3-CNLS equation can be used to investigate the optical soliton propagation in three-core fibers, which contain some potential applications in the optical fiber communication system. Using the Darboux transformation method with computer simulation, the two-bright boomerang soliton solutions are attained analytically for the dispersion and nonlinearity functions. The propagation and interaction properties of boomerang solitons are investigated, while the variable coefficients are adopted as linear functions. Various interaction scenarios are illustrated by plotted figures to reveal the importance of obtained soliton solutions. The physical significance of boomerang solitons can be understood from the displayed figures. The obtained results will be benefit soliton path control and soliton phase management in an inhomogeneous three-core optical fiber.

Conservation laws and breather-to-soliton transition for a variable-coefficient modified Hirota equation in an inhomogeneous optical fiber

Optical fibers are used in the communications, biological sensors and chemical sensors. We investigate a variable-coefficient modified Hirota equation for the amplification or absorption of pulses propagating in an inhomogeneous optical fiber. With respect to the complex envelope of the optical field, we construct the infinitely-many conservation laws based on the existing Lax pair. According to the existing Darboux transformation, we derive the three-soliton solutions, the higher-order breather solutions and breather-to-soliton transition condition. Amplitudes of the two solitons change after the interaction, while velocities of them are unchanged via asymptotic analysis. When P ( z ) = 0 , interactions among the three parabolic or wavy solitons, interaction between the two parabolic or wavy or crooked breathers, and interactions among the three parabolic and wavy breathers are presented, where P ( z ) is related to the nonlinear focus length. Velocities of three solitons or two crooked breathers with P ( z ) ≠ 0 are different from those with P ( z ) = 0 . Based on the breather-to-soliton transition condition, when P ( z ) = 0 , parabolic or wavy multi-peak and M-shaped solitons are presented; when P ( z ) ≠ 0 , the crooked periodic wave and anti-dark soliton are shown.