arXiv subjects

Houria Triki

Publications and source records attributed to Houria Triki.

16 recordsLinked to original sources

arXiv2026

Self-similar vector solitons for the coupled higher-order nonlinear Schrodinger equations in inhomogeneous optical fibers

We prove the existence of two kinds of self-similar vector solitons in an inhomogeneous optical fiber medium, where light propagation is governed by a pair of coupled higher-order nonlinear Schrodinger equations with varying second- and third-order dispersions, self- and cross-phase modulation non linearities, self-steepening, and linear gain/loss effects. The newly found self-similar waves comprise bright-W-shaped and kink-antikink waveforms with nonvanishing amplitudes. As a practical exam ple, we discuss the propagation dynamics of these soliton structures in a periodically distributed fiber system as well as an exponential dispersion-decreasing fiber. The results demonstrate that the parameter functions of gain/loss and third-order dispersion serve as a key factor in determining the nonlinear dynamics of self-similar vector solitons. In particular, we find that precise control over the shape and dynamic evolution of self-similar pulses can be achieved through a proper choice of the distributed third-order dispersion parameter, while the gain/loss coefficient controls their intensity.

nlin.PS↗

arXiv2026

Solitons and periodic wave solutions for complex Ginzburg-Landau equation modelling fiber lasers and nonequilibrium phenomena

New types of soliton and periodic waves are identified for a nonlinear dissipative medium where the pulse propagation is governed by the cubic complex Ginzburg-Landau equation. We find that the dynamical equation for the pulse amplitude supports two distinct types of kink and antikink solitons with different functional forms. It is found that the obtained kink and antikink soliton waveforms occur under the same fixed inverse velocity. The results also indicate that the periodic waves can propagate with variety of wave forms such as sn, cn, dn and their rational forms as well. It is also shown that in the long-wave limit, the derived periodic waves degenerate into different bright and dark soliton pulses. The stability analysis based on the theory of dispersive waves in nonlinear optics is developed. It is shown that some elliptic and soliton solutions are quasi-stable in the context of passive mode locking lasers described by complex Ginzburg-Landau equation.

nlin.PS↗

arXiv2025

Quantum Dynamics and Elementary Excitations in Superfluid He4 Films at Low Temperatures

We have formulated a novel quantum nonlinear Schrodinger equation describing of superfluid He4 in films at low temperatures. It is shown that in classical limit the found nonlinear Schrodinger equation reduces to a system of equations which are equivalent to Boussinesq equations describing the propagation of long gravity waves in incompressible fluids. This nonlinear Schrodinger equation leads to phonon-roton dispersion relation for elementary excitations in superfluid He4 films at low temperatures. The quartic soliton, dark soliton, cosine and elliptic periodic wave solutions are obtained analytically as weakly excited quantum waves propagating in He4 films. We have also shown numerically that the presented nonlinear Schrodinger equation describes the quartic and dark solitary waves in helium films. These solitary and periodic quantum waves can find numerous important practical applications.

quant-ph↗

arXiv2025

Pulse-train propagation in nonlinear Kerr media governed by higher-order dispersion

We discover three novel classes of pulse-train waveforms in an optical Kerr nonlinear medium possessing all orders of dispersion up to the fourth order. We show that both single- and double humped pulse-trains can be formed in the nonlinear medium. A distinguishing property is that these structures have different amplitudes, widths and wavenumbers but equal velocity which depends on the three dispersion parameters. More importantly, we find that the relation between the amplitude and duration of all the newly obtained pulse-trains is determined by the sign of a joint parameter solely. The results show that those optical waves are general, in the sense that no specified conditions on the material parameters are assumed. Considering the long-wave limit, the derived pulse-trains degenerate to soliton pulses of the quartic and dipole kinds.

nlin.PS↗

arXiv2024

Stopping of generalized solitary and periodic waves in optical waveguide with varying and constant parameters

We demonstrate the possibility of stopping the soliton pulses in optical waveguide with varying and constant parameters exhibiting a Kerr nonlinear response. By using the similarity transformation, we have found the constraint condition for varying waveguide parameters and derive the exact analytical solutions for self-similar bright, kink, dark and rectangular solitary and periodic waves for nonlinear Schr\"{o}dinger equation with variable coefficients. All these generalized wave solutions depend on five arbitrary parameters and two free integration constants. It is found that the velocity of solitons is related to a free parameter $q$, which play an important role in the dynamic behavior of soliton's evolution. The precise expression of soliton's velocity shows that the solitons can be nearly stopped for appropriate values of free parameter $q$. The possibility for stopping of soliton pulses can also be realized when all parameters of nonlinear Schr\"{o}dinger equation are constant. The numerical simulations show that the stopping behavior of solitons and rectangular solitary waves can be achieved for appropriate values of free parameters characterizing these wave solutions.

nlin.PS↗

arXiv2024

Generation of solitons and periodic wave trains in birefringent optical fibers

We investigate the existence and propagation properties of all possible types of envelope soliton pulses in a birefringent optical fiber wherein the light propagation is governed by two coupled nonlinear Schrodinger equations with coherent and incoherent nonlinear couplings. Especially, we study the existence of optical solitons under the influence of group-velocity dispersion and third-order nonlinearity, which have physical relevance in the context of elliptical core optical fiber. The results show that the waveguiding medium supports the existence of a wide variety of propagating envelope solitons, including dipole-bright, bright-dipole, bright-dark, dark-bright, W-shaped-dipole and dipole-W-shaped pulses which exhibit different characteristics. Interestingly, we find that the obtained soliton pairs are allowable in both the normal and anomalous dispersion regimes. A wide class of exact analytic periodic (elliptic) wave solutions are identified. This illustrates the potentially rich set of localized pulses and nonlinear periodic waves in birefringent optical fiber media.

nlin.PS↗

arXiv2023

Wave-speed management of dipole, bright and W-shaped solitons in optical metamaterials

Wave-speed management of soliton pulses in a nonlinear metamaterial exhibiting a rich variety of physical effects that are important in a wide range of practical applications, is studied both theoretically and numerically. Ultrashort electromagnetic pulse transmission in such inhomogeneous system is described by a generalized nonlinear Schreodinger equation with space-modulated higher-order dispersive and nonlinear effects of different nature. We present the discovery of three types of periodic wave solutions that are composed by the product of Jacobi elliptic functions in the presence of all physical processes. Envelope solitons of the dipole, bright and W-shaped types are also identified, thus illustrating the potentially rich set of localized pulses in the system. We develop an effective similarity transformation method to investigate the soliton dynamics in the presence of the inhomogeneities of media. The application of developed method to control the wave speed of the presented solitons is discussed. The results show that the wave speed of dipole, bright and W-shaped solitons can be effectively controlled through spatial modulation of the metamaterial parameters. In particular, the soliton pulses can be decelerated and accelerated by suitable variations of the distributed dispersion parameters.

nlin.PS↗

arXiv2023

Propagation of coupled quartic and dipole multi-solitons in optical fibers medium with higher-order dispersions

We present the discovery of two types of multiple-hump soliton modes in a highly dispersive optical fiber with a Kerr nonlinearity. We show that multi-hump optical solitons of quartic or dipole types are possible in the fiber system in the presence of higher-order dispersion. Such nonlinear wave packets are very well described by an extended nonlinear Schrodinger equation involving both cubic and quartic dispersion terms. It is found that the third- and fourth-order dispersion effects in the fiber material may lead to the coupling of quartic or dipole solitons into double-, triple-, and multi-humped solitons. We provide the initial conditions for the formation of coupled multi-hump quartic and dipole solitons in the fiber. Numerical results illustrate that propagating multi-quartic and multi-dipole solitons in highly dispersive optical fibers councide with a high accuracy to our analytical multi-soliton solutions. It is important for applications that described multiple-hump soliton modes are stable to small noise perturbation that was confirmed by numerical simulations. These numerical results confirm that the newly found multi-soliton pulses can be potentially utilized for transmission in optical fibers medium with higher-order dispersions.

nlin.PS↗

arXiv2022

Periodic and solitary waves generating in optical fiber amplifiers and fiber lasers with distributed parameters

We study self-similar dynamics of picosecond light pulses generating in optical fiber amplifiers and fiber lasers with distributed parameters. A rich variety of periodic and solitary wave solutions are derived for the governing generalized nonlinear Schr\"{o}dinger equation with varying coefficients in the presence of gain effect. The constraint on distributed optical fiber parameters for the existence of these wave solutions is presented. The dynamical behaviour of those self-similar waves is discussed in a periodic distributed amplification system. The stability of periodic and solitary wave solutions is also studied numerically by adding white noise. It is proved by using the numerical split-step Fourier method that the profile of these nonlinear self-similar waves remains unchanged during evolution.

physics.optics↗

arXiv2022

Propagation of periodic and solitary waves in a highly dispersive cubic-quintic medium with self-frequency shift and self-steepening nonlinearity

We study the dynamics of femtosecond light pulse propagation in a cubic-quintic medium exhibiting dispersive effect up to the fourth order as well as self-frequency shift and self-steepening nonlinearity. A rich variety of periodic and solitary wave solutions are derived for the governing generalized higher-order nonlinear Schr\"{o}dinger equation in the presence of self-frequency shift and self-steepening effects. It is found that the frequency shift, inverse velocity, amplitude and wave number of both periodic and solitary waves depend on dispersion coefficients and nonlinearity parameters as well. The conditions on optical fiber parameters for the existence of these structures are presented. The stability of these periodic and solitary wave solutions is studied numerically by adding white noise. It is proved by using the numerical split-step Fourier method that the profile of these nonlinear waves remains unchanged during evolution.

nlin.PS↗

arXiv2022

Periodic and localized waves in parabolic-law media with third- and fourth-order dispersions

We study the propagation of femtosecond light pulses inside an optical fiber medium exhibiting higher-order dispersion and cubic-quintic nonlinearities. Pulse evolution in such system is governed by a higher-order nonlinear Schr% \"{o}dinger equation incorporating second-, third-, and fourth-order dispersions as well as cubic and quintic nonlinearities. Novel classes of periodic wave solutions are identified for the first time by means of an appropriate equation method. Results presented indicated the potentially rich set of periodic waves in the system under the combined influence of higher-order dispersive effects and cubic-quintic nonlinearity. Solitary waves of both bright and dark types are also obtained as a limiting case for appropriate periodic solutions. It is found that the velocity of these structures is uniquely dependent on all orders of dispersion. Conditions on the optical fiber parameters for the existence of these stable nonlinear wave-forms are presented as well.

nlin.PS↗

arXiv2022

Breather and interacting soliton and periodic waves for modified KdV equation

We present the discovery of a class of exact spatially localized as well as periodic wave solutions within the framework of the modified Korteweg-de Vries equation. This class comprises breather and interacting soliton solutions as well as interacting periodic wave solutions. The functional forms of these solutions include a joint parameter which can take both positive and negative values of unity. It is found that the existence of those closed form solutions depend strongly on whether the cubic nonlinearity parameter should be considered positive or negative. The derived wave structures show interesting properties that may find practical applications.

nlin.PS↗

arXiv2022

Novel solitary and periodic waves in quadratic-cubic non-centrosymmetric waveguides

We present a wide class of novel solitary and periodic waves in a non-centrosymmetric waveguide exhibiting second- and third-order nonlinearities. We show the existence of bright, gray, and W-shaped solitary waves as well as periodic waves for extended nonlinear Schr\"{o}dinger equation with quadratic and cubic nonlinearities. We also obtained the exact analytical algebraic-type solitary waves of the governing equation, including bright and W-shaped waves. The results illustrate the propagation of potentially rich set of nonlinear structures through the optical waveguiding media. Such privileged waveforms characteristically exist due to a balance among diffraction, quadratic and cubic nonlinearities.

nlin.PS↗

arXiv2021

Chirped periodic and solitary waves in nonlinear negative index materials

Propagation of ultrashort pulses at least a few tens of optical cycles in duration through a negative index material is investigated theoretically based on the generalized nonlinear Schrödinger equation with pseudo-quintic nonlinearity and self-steepening effect. Novel periodic waves of different forms are shown to exist in the system in the presence of higher-order effects. It is found that such periodic structures exhibit an interesting chirping property which depends on the light field intensity. The nonlinearity in pulse chirp is found to be caused by the presence of self-steepening effect in the negative index medium. The solutions also comprise dark, bright, and kink solitary waves. Stability of the solitary wave solutions are proved analytically using the theory of nonlinear dispersive waves. The stability of the solutions is numerically studied under finite initial perturbations.

nlin.PS↗

arXiv2021

Chirped periodic and localized waves in a weakly nonlocal media with cubic-quintic nonlinearity

We study the propagation of one-dimentional optical beams in a weakly nonlocal medium exhibiting cubic-quintic nonlinearity. A nonlinear equation governing the evolution of the beam intensity in the nonlocal medium is derived thereby which allows us to examine whether the traveling-waves exist in such optical material. An efficient transformation is applied to obtain explicit solutions of the envelope model equation in the presence of all material parameters. We find that a variety of periodic waves accompanied with a nonlinear chirp do exist in the system in the presence of the weak nonlocality. Chirped localized intensity dips on a continuous-wave background as well as solitary waves of the bright and dark types are obtained in a long wave limit. A class of propagating chirped self-similar solitary beams is also identified in the material with the consideration of the inhomogeneities of media. The applications of the obtained self-similar structures are discussed by considering a periodic distributed amplification system.

nlin.PS↗

arXiv2019

Propagation of dipole solitons in inhomogeneous highly dispersive optical fiber media

We consider the ultrashort light pulse propagation through an inhomogeneous monomodal optical fiber exhibiting higher-order dispersive effects. Wave propagation is governed by a generalized nonlinear Schrödinger equation with varying second-, third-, and fourth-order dispersions, cubic nonlinearity, and linear gain or loss. We construct a new type of exact self-similar soliton solutions that takes the structure of dipole via a similarity transformation connected to the related constant-coefficients one. The conditions on the optical fiber parameters for the existence of these self-similar structures are also given. The results show that the contribution of all orders of dispersion is an important feature to form this kind of self-similar dipole pulse shape. The dynamic behaviors of the self-similar dipole solitons in a periodic distributed amplification system are analyzed. The significance of the obtained self-similar pulses is also discussed.

nlin.PS↗