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This research aims to conduct a comprehensive qualitative and quantitative analysis of Kudryashov’s equation with third-order dispersion. Initially, the equation is converted into a two-dimensional dynamic system through the application of the traveling wave transformation. The generalized trial equation method is then utilized to derive Gaussian soliton solutions. Furthermore, the existence of periodic and soliton solutions in the equation is established by utilizing the burification method. The conclusions of the theoretical analysis are validated by constructing exact solutions, and the modulation instability of the equation is also explored. Moreover, by introducing various perturbation terms, we investigate the chaotic properties of the equations under different perturbation terms. This research represents the first thorough investigation of all possible traveling wave solutions for Kudryashov’s equation with third-order dispersion, and also uncovers notable chaotic behavior under specific perturbation scenarios.

This work deals with a new ( 3 + 1 ) -dimensional Painlevé integrable fifth-order equation characterized by third-order temporal and spatial dispersions. The Painlevé test is carried out to demonstrate the complete integrability of this model. A rule that governs the dispersion relation with the spatial variables coefficients is reported. We employ the simplified Hirota’s method to obtain multiple soliton solutions. We examine specific cases of the dispersion relations along with their respective coefficients. It is hoped that the results reported in this work can enrich applications in solitary waves theory, and more specifically, in models with third-order temporal dispersion.

In this work, a dispersion compensating photonic crystal fiber (DC-PCF) is proposed in which dispersion, dispersion slope, second order dispersion, third order dispersion, nonlinearity, effective mode area, parameter are investigated. The suggested structure is very effective for compensating of chromatic dispersion about −951 to −3075.10 ps/(nm.km) over 1340–1640 nm wavelength bandwidth. With perfectly matched layer boundary condition, guiding properties are inspected applying finite element method (FEM). The investigated results conform the opportunity of large negative dispersion and high group velocity dispersion (GVD) of −2367.10 ps/(nm.km) and 3018.55 ps /km respectively, at 1550 nm operating wavelength. The offered fiber also shows low third order dispersion about −637.88 ps /km, high nonlinearity of 91.11 W  km . From overall simulation results, it can be expected that the suggested PCF will be an effective candidate in high bit rate long haul optical communication system as well as sensing applications.

We have investigated the robustness of the rogue wave solutions of two reductions of the generalized nonlinear Schrödinger equation with the third-order dispersion perturbation term. The two reductions are the nonlinear Schrödinger (NLS) equation and the second-type derivative nonlinear Schrödinger (DNLSII) equation. The perturbed equations have practical physical application value. However, they are non-integrable so their exact rogue wave solutions can hardly be obtained by analytical methods. In this paper, we use numerical methods to simulate the perturbed rogue wave solutions and use the quantitative analysis method to assess the robustness of the rogue wave solutions. Two criteria c and r are defined based on the definition of rogue waves in ocean science to analyze the distortion degree of rogue waves quantitatively. The numerical simulation results and the values of these criteria show that the rogue wave solutions of these two reductions are robust under the third-order dispersion perturbation, while the rogue wave solution of the DNLSII equation is more sensitive to the perturbation than that of the NLS equation.

In ultra-short laser pulses, small changes in dispersion properties before the final focusing mirror can lead to severe pulse distortions around the focus and therefore to very different pulse properties at the point of laser–matter interaction, yielding unexpected interaction results. The mapping between far- and near-field laser properties intricately depends on the spatial and angular dispersion properties as well as the focal geometry. For a focused Gaussian laser pulse under the influence of angular, spatial and group-delay dispersion, we derive analytical expressions for its pulse-front tilt, duration and width from a fully analytic expression for its electric field in the time–space domain obtained with scalar diffraction theory. This expression is not only valid in and near the focus but also along the entire propagation distance from the focusing mirror to the focus. Expressions relating angular, spatial and group-delay dispersion before focusing at an off-axis parabola, where they are well measurable, to the respective values in the pulse’s focus are obtained by a ray tracing approach. Together, these formulas are used to show in example setups that the pulse-front tilts of lasers with small initial dispersion can become several tens of degrees larger in the vicinity of the focus while being small directly in the focus. The formulas derived here provide the analytical foundation for observations previously made in numerical experiments. By numerically simulating Gaussian pulse propagation and measuring properties of the pulse at distances several Rayleigh lengths off the focus, we verify the analytic expressions.

This article presents the propagation of solitons in linear birefringent single-mode fibers under the influence of third-order dispersion. The behaviour of two partial pulses evolved due to polarization mode dispersion is investigated under the presence of third-order dispersion (TOD). The analytical solutions to coupled nonlinear Schrödinger equations (CNLSE) with TOD are derived using multiple scale perturbation expansion and the results are compared with the solutions obtained using split-step Fourier method to find the effects of TOD on soliton propagation. It is found that the resultant soliton deviates from its initial position with third-order dispersion and this deviation is considerably small when the pulse propagates relatively far from the zero-dispersion wavelength. It is observed that the behaviour of two partial pulses and their subsequent properties depend not only on the fiber parameters, but also on the amplitude of the launched soliton pulses.

This study aims to update the existing SG PW laser system and improve the temporal contrast and shape fidelity of a compressed pulse with a 150 fs level for multi-PW (5–10 PW). The design of third-order dispersion (TOD) compensation via a birefringent crystal was studied through numerical simulations and experiments. The dispersions introduced by the birefringent crystal were calculated using the Jones matrix element by changing the in-plane rotation angle ϕ, thickness d, incident angle θ, and temperature T, while also considering the transmission spectral bandwidth. The group-velocity dispersion (GVD), TOD, and fourth-order dispersion (FOD) of the existing SG PW laser system and its influence on the compressed pulse with different pulse durations were analyzed. The results suggest that a TOD of 1.3×106 fs3 needs to compensate for the multi-PW design. The compensation scheme is designed using a quartz crystal of d = 6.5 mm, θ = 90°, ϕ = 17°, and T = 21 °C, corresponding to the thickness, inclination angle, in-plane rotation angle, and temperature, respectively. Furthermore, we show a principle-proof experiment offline and measure the GVD and TOD by the Wizzler, which is based on theoretical simulations. These results can be applied to independently and continuously control the TOD of short-pulse laser systems.

This paper discusses novel approaches to the numerical integration of the coupled nonlinear Schrödinger equations system for few-mode wave propagation. The wave propagation assumes the propagation of up to nine modes of light in an optical fiber. In this case, the light propagation is described by the non-linear coupled Schrödinger equation system, where propagation of each mode is described by own Schrödinger equation with other modes’ interactions. In this case, the coupled nonlinear Schrödinger equation system (CNSES) solving becomes increasingly complex, because each mode affects the propagation of other modes. The suggested solution is based on the direct numerical integration approach, which is based on a finite-difference integration scheme. The well-known explicit finite-difference integration scheme approach fails due to the non-stability of the computing scheme. Owing to this, here we use the combined explicit/implicit finite-difference integration scheme, which is based on the implicit Crank–Nicolson finite-difference scheme. It ensures the stability of the computing scheme. Moreover, this approach allows separating the whole equation system on the independent equation system for each wave mode at each integration step. Additionally, the algorithm of numerical solution refining at each step and the integration method with automatic integration step selection are used. The suggested approach has a higher performance (resolution)—up to three times or more in comparison with the split-step Fourier method—since there is no need to produce direct and inverse Fourier transforms at each integration step. The key advantage of the developed approach is the calculation of any number of modes propagated in the fiber.

Radio over is an attractive solution for broadband wireless access. In this paper, the performance of externally and direct intensity modulated RoF links is analyzed in the presence of the group velocity dispersion and third-order dispersion of the optical fiber. An external modulation system with dual electrode lithium niobate Mach–Zehnder modulator (DE-MZM) and direct modulation system with vertical-cavity surface-emitting laser (VCSEL) are considered. Both modulation schemes are tested using Gaussian optical pulses. Simulations are performed with the same values for common global parameters for both schemes. Although external modulation is a generally considered more advanced, our simulations show that the direct modulation technique with VCSEL shows a more robust performance. The performances are compared using performance parameters like Q factor, eye diagram, BER and RF signal amplitude.

In this paper, the decay of higher order soliton in the presence of third order dispersion, intrapulse Raman scattering and self-steepening scattering has been examined in optical fiber soliton communication. The result has been analysed in the form of graphic representation for optical time domain visualizer and optical spectrum analyzer.