Nonlinear Dispersion Research Articles

Wave Propagation and Bottom Deformation in the Coastal Zone of the Sea Within the Framework of the Nonlinear Dispersion Theory of Shallow Water

Wave Propagation and Bottom Deformation in the Coastal Zone of the Sea Within the Framework of the Nonlinear Dispersion Theory of Shallow Water

Electroelastic wave dispersion in the rotary piezoelectric NEMS sensors/actuators via nonlocal strain gradient theory

This article introduces a computational means for investigating the electroelastic nonlinear wave dispersion traits of the nano-dimension sandwich pipe, which is composed of a core formed of a bi-directional functionally graded (Bi-FG) material, together with a piezoelectric sensor/actuator. A combination of Hamilton’s principle, first-order shear deformation, along with Von-Karman nonlinearity, is used for modeling and obtaining the nonlinear governing equations of the nano-sized sandwich pipe connected to a piezoelectric part. The nonlinear governing equations to obtain the nonlinear phase velocity of the current system are determined using a combination of analytical and multiple scales approaches. Due to some computational cost for choosing the precise values of both the nonlocality factor and length scale of the nanopipe in the laboratory, for the first time in this research, with the aid of COMSOL multi-physics finite element simulation, the results are verified, and new outcomes for obtaining the exact functions for nonlocal and length scale factors is presented. In addition, an artificial neural network (ANN) is utilized in this study for the prediction of the results. The mathematical and finite element results were used to train the ANN. A newly presented optimization algorithm is exploited for the first time for optimizing the ANN parameters concluding higher accuracy of the ANN predictions. Consequently, to explore the influences of the location of the piezoelectric patch, nonlocality and length scale factors, and applied voltage parameter on the phase velocity characteristics of the nano-dimension sandwich pipe made of a Bi-FG core and electrically patch, an effort is performed. As an applicable result that can be useful in the related nano-industries, the current work presents exact nonlocal and length scale functions for different conditions.

Analysis of performance limits in optical communications due to fiber nonlinearity and third order dispersion

In this study, an analysis is conducted to treasure the expressions of the pulsation expansion factor, in addition to the standardized output, and solve the nonlinear Schrödinger equation (NLSE), reflecting the impact of XPM on third order dispersion. Using large effective area fiber (LEAF) and standard single-mode fiber (SSMF), the effects of transmission distances and varying input powers are assessed at various transmission speeds. The first and second order GVD XPM effects are the only factors influencing the pulse’s propagation. The second-order effects of GVD are not noticeable at short distances and low bit rates, but they become noticeable and impact system performance as the bit rate increases. The study discovered that input dominance has less of an impact on pulse width than data rate and fiber length. Methodical derivation and numerical simulation using the split-phase Fourier method at the same data rate and input power yield the SSMF and LEAF consequences. In comparison to LEAF fibers, XPM has a greater beneficial impact on second and third order dispersion in SSMF fibers.

Extraction of Solitons in Optical Fibers for the (2+1)-Dimensional Perturbed Nonlinear Schrödinger Equation Via the Improved Modified Extended Tanh Function Technique

The presented research investigates the (2+1)-dimensional perturbed nonlinear Schrödinger model. This model takes into account various effects such as fourth order dispersion, intermodal dispersion, nonlinear dispersion, group velocity dispersion, Kerr nonlinearity and self steepening effects. This model simulates the estimation of optical solitons and a variety of broadcasting networks’ transmission in nonlinear fiber optics. The proposed model is studied using the improved modified extended tanh function technique. For the proposed model, several solitons and other solutions are generated. These solutions including {bright, dark and singular} solitons, singular periodic and Jacobi elliptic solutions. By introducing the two- and three-dimensional graphs, the physical behavior of the retrieved solutions is displayed.

Numerical analysis of microstructured optical fibers based on flint glass for ultra-high nonlinearity, low loss, and broadband dispersion compensation across telecom bands

This research investigates the potential of flint glass as a foundational material for photonic crystal configurations designed to achieve high nonlinear coefficients across various communication wavelengths. We explore dispersion management within telecom bands using flint glass-based micro-structured optical fibers, employing numerical analysis via the finite element method to assess optical properties. In this study, three different basic MOF structures (hexagonal, square, and octagonal) were created using flint glass background material rather of the commonly utilized fused silica material, and the numerically was assessed in contrast to prior studies and designs. Among the configurations studied, the octagonal arrangement (FGO-MOF) excels in dispersion compensation, achieving −136.6 ps/(nm.km) at 1.55 µm. Conversely, the hexagonal air hole ring cladding design (FGH-MOF) displays higher nonlinearity (770.5 W−1.km−1), a smaller effective area (1.115 µm2), and a high numerical aperture (0.6378). In contrast, the square air hole ring cladding optical fiber (FGS-MOF) exhibits low confinement loss (6.309 × 10−7 dB/cm) at 1.55 µm but with comparatively less favorable optical properties. Our study demonstrates that the hexagonal microstructured optical fiber with flint glass (FGH-MOF) offers superior performance in dispersion compensation, nonlinearity, and low loss within telecom bands. This finding suggests promising applications in high-bit-rate communication systems, biomedical sensing, and supercontinuum generation, presenting exciting avenues for further research and practical implementation.

Nonlinear wave dispersion in monoatomic chains with lumped and distributed masses: discrete and continuum models

Nonlinear wave dispersion in monoatomic chains with lumped and distributed masses: discrete and continuum models

Nonlinear theory of the modulational instability at the ion–ion hybrid frequency and collapse of ion–ion hybrid waves in two-ion plasmas

We study the dynamics of two-dimensional (2D) nonlinear ion–ion hybrid waves propagating perpendicular to an external magnetic field in plasmas with two ion species. We derive nonlinear equations for the envelope of electrostatic potential at the ion–ion hybrid frequency to describe the interaction of ion–ion hybrid waves with low-frequency acoustic-type disturbances. The resulting nonlinear equations also take into account the contribution of the second harmonics of the ion–ion hybrid frequency. A nonlinear dispersion relation is obtained, and, for a number of particular cases, modulational instability growth rates are found. By neglecting the contribution of second harmonics, the phenomenon of the collapse of ion–ion hybrid waves is predicted. It is shown that taking into account the interaction with the second harmonic results in the existence of a stable two-dimensional soliton.

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.

Explicit optical solitons of a perturbed Biswas–Milovic equation having parabolic-law nonlinearity and spatio-temporal dispersion

This paper deals with a new variant of the Biswas–Milovic equation, referred to as the perturbed Biswas–Milovic equation with parabolic-law nonlinearity in spatio-temporal dispersion. To our best knowledge, the considered equation which models the pulse propagation in optical fiber is studied for the first time, and the abundant optical solitons are successfully obtained utilizing the auxiliary equation method. Utilizing a wave transformation technique on the considered Biswas–Milovic equation, and by distinguishing its real and imaginary components, we have been able to restructure the considered equation into a set of nonlinear ordinary differential equations. The solutions for these ordinary differential equations, suggested by the auxiliary equation method, include certain undetermined parameters. These solutions are then incorporated into the nonlinear ordinary differential equation, leading to the formation of an algebraic equation system by collecting like terms of the unknown function and setting their coefficients to zero. The undetermined parameters, and consequently the solutions to the Biswas–Milovic equation, are derived by resolving this system. 3D, 2D, and contour graphs of the solution functions are plotted and interpreted to understand the physical behavior of the model. Furthermore, we also investigate the impact of the parameters such as the spatio-temporal dispersion and the parabolic nonlinearity on the behavior of the soliton. The new model and findings may contribute to the understanding and characterization of the nonlinear behavior of pulse propagation in optical fibers, which is crucial for the development of optical communication systems.

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.

Design method for eliminating spectral line tilt in a multiple sub-pupil ultra-spectral imager (MSPUI).

A multiple sub-pupil ultra-spectral imaging system designed with a single spectrometer and detector can simultaneously detect multiple-channel spectra with ultra-high spectral resolution. However, due to using a prism in the system's front end, the nonlinear dispersion introduces spectral line tilt in the imaging spectra. This phenomenon can lead to bias in the final spectral data. To eliminate this issue, we propose a new design by introducing a second prism to correct this spectral tilt in the system. The angle of spectral line tilt generated by the nonlinear dispersion of the first prism is derived. It provides the theoretical basis for characterizing the second complementary prism. Finally, a UV multiple sub-pupil ultra-spectral imaging system is designed. The system employs two pupil separation prisms and one flat panel array to segment the pupil in three channels, each operating within spectral ranges of 180∼210 nm, 275∼305 nm, and 370∼400 nm, respectively. The spectral resolutions in all three channels are better than 0.1 nm. The corrected spectral line tilt is less than 1/3 of a pixel in the two channels with pupil separation prisms. At a Nyquist frequency of 30 lp/mm, the modulation transfer functions of all three channels are greater than 0.7, ensuring imaging quality. The design results indicate that the method proposed in this paper, utilizing complementary prisms, can effectively correct the spectral line tilt caused by the nonlinear dispersion of the pupil separation prisms. This design approach can be a reference for developing multiple sub-pupil ultra-spectral imaging systems.

Nonlinear dispersion relation of dust acoustic waves using the Korteweg–de Vries model

In this Brief Communication, we present an exact analytic nonlinear dispersion relation (NLDR) for the dust acoustic waves using the Korteweg–de Vries model. The NLDR agrees with the spectrum of spatiotemporal evolution obtained from an exact solution as in Mir et al. [Phys. Plasmas 27, 113701 (2020)]. The NLDR also shows a reasonable match with the experimental data of Thompson et al. [Phys. Plasmas 4, 2331 (1997)] in the long-wavelength limit (kλD≪1). We suggest that such nonlinear corrections should be incorporated in the dispersion relation along with damping, streaming, and correlation effects in order to provide a more realistic interpretation of experimental data.

Nonlinear elastic wave dispersions of solar cells strengthened by advanced functionally graded materials via both mathematical modeling and deep neural networks technique

From claims of roughly 3 % efficiency in 2009 to over 25 % efficiency now, perovskite solar cells have made amazing developments in recent years. Perovskite solar cells have quickly increased their efficiency, but there are still a number of obstacles to overcome before they can be considered a viable commercial technology. So, improving the stability of the perovskite solar cells and obtaining the mechanical properties of this kind of structure using computer simulation to decrease the computational cost is a challenging issue for designers. In this work, instead of a metal layer in the fabrication of solar cells, a functionally graded (FG) layer in which the material properties in this layer change in each direction. For the first time in the current report, the nonlinear phase velocity of the 3D-FG solar cells via mathematical simulation is presented. For solving the nonlinear partial differential equations (PDEs) of the perovskite solar cells, an analytical method is used. After doing some mathematical manipulation using the analytical method, a multiple scales method for solving the nonlinear equations in the time domain is presented. In order to compensate for the absence of a dataset suitable for deep neural networks (DNN), a mathematical simulation is conducted to acquire the nonlinear phase velocity characteristics of enhanced solar cells. The DNN method is used to forecast the nonlinear phase velocity characteristics of the present study, after the completion of training, testing, and validation processes. This approach has the advantage of cheap computing expense. Finally, the results show that when the panels tend to be too concave or convex, the nonlinear phase velocity is unstable. As an amazing outcome for related industries, the nonlinear phase velocity is very sensitive to the values of Kx, Ky, and Rx/a, and all designers according to their purposes should consider the amount of these parameters. The current results’ outcomes can be used in future building of the perovskite solar cell knowing about nonlinear dynamics features of 3D-FG perovskite solar cells.

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.

Optical and optoelectronic properties of gallium oxide films fabricated by the chemical vapour deposition method

The present work investigated the influence of growth time on the structural, optical, and optoelectronic properties of β-Ga2O3 films produced on Si substrates by the chemical vapour deposition method. The prepared films were characterized by X-ray diffraction, field-emission scanning electron microscope, and UV–Vis spectrophotometer. The films exhibited a mixed phase (β-α)-Ga2O3 crystal structure. The crystallite size ranged between 34.98 and 164.69 nm. The bandgap increased from 4.74 to 4.88 eV. The absorption and extinction coefficients were in the orders of 103 and 10−1, respectively. The refractive index, dispersive energy and single oscillator energy increased from 1.86 to 1.87, 19.24 to 28.64, and 8.36 to 9.54, respectively, with an increase of growth time. The oscillator strength, oscillator wavelength, third-order nonlinear optical susceptibility and dispersion of refractive index were in the orders of 10−4, 10−2, 10−10 and 10−9, respectively. The carrier concentration, optical conductivity, optical mobility, and optical resistivity were also evaluated. The real and imaginary dielectric constants, and plasmon frequency were also determined.

Manifestation of varying polarization state of alternating channels in multicasting WDM network and mitigating the impairments using nonlinear OPC and dispersion compensation

Manifestation of varying polarization state of alternating channels in multicasting WDM network and mitigating the impairments using nonlinear OPC and dispersion compensation

On the importance of heavy fields in pseudo-scalar inflation

Pseudo-scalar inflation coupled with U(1) gauge fields through the Chern-Simons term has been extensively studied. However, new physics arising from UV theories may still influence the pseudo-scalar field at low-energy scales, potentially impacting predictions of inflation. In the realm of effective field theory (EFT), we investigated axion inflation, where operators from heavy fields are also present, in addition to the axion and gauge fields. The integrated out fields have two significant effects: the non-linear dispersion regime and coupling heavy modes to the Chern-Simons term. The first effect changes the propagation of the curvature fluctuation, while the second one results in additional operators that contribute to curvature fluctuation via inverse decay. We derived the power spectrum and magnitude of equilateral non-Gaussianity in this low-energy EFT. We found that the second effect could become significant as the mass of heavy fields approaches Hubble scale.

Necessary conditions for convex-periodic, elliptic-periodic, inclined-periodic, and rogue wave-solutions to exist for the multi-dispersions Schrodinger equation

In this study, we revisit the modified Schrödinger equation, which incorporates multiple dispersion terms, including linear, nonlinear, and random dispersion. We establish the essential constraints on the model’s parameters to ensure the presence of complex-valued solutions. Subsequently, we employ effective and explicit techniques such as the extended tanh-coth expansion, rational sine-cosine functions, and rational sinh-cosh functions to derive innovative types of periodic solutions for the proposed model. These solutions demonstrate unique physical properties applicable to various complex media, such as surface water waves, optical fiber pulses, and plasma waves.

New soliton solutions and modulation instability analysis of the regularized long-wave equation in the conformable sense

In this manuscript, we explore the solitary soliton of the regularized long-wave (RLW) equation which involving with weedy nonlinearity effects and dispersion relations which arises in shallow water, phonon packets in crystals, plasma wave and ion auditory waves. To execute the soliton solutions, we applied the advance Exp( − φ(ξ)) expansion method and the new form of modified Kudryashov's technique with conformable derivative from the fractional RLW model. For the explanation of the nature of RLW model, we obtained some behavior such as on the obtained solitons as bell-wave, rogue wave, periodic and double-periodic waves. This article offered the effects of conformable derivative to check the stability of the obtained phenomena. To check the stability of this model, we use the modulation instability analysis also. This work has a decent sense to endorse the extensive proposal of the model. Some 3-D and 2-D plots with their graphical explanation provides this research to characterized the obtained waves of RLW model.

Novel closed-form analytical solutions and modulation instability spectrum induced by the Salerno equation describing nonlinear discrete electrical lattice via symbolic computation

A nonlinear electrical lattice is an effective experimental tool for dealing with nonlinear dispersive media and creating possibilities for the realistic modeling of electrical soliton. In this work, we discuss the dynamical behavior of the governing (1+1)-dimensional time–space Salerno equation, which describes the discrete electrical lattice with nonlinear dispersion. The different kinds of solutions in the form of periodic, Jacobi elliptic, and exponential functions are obtained by the two analytical approaches, namely the modified generalized exponential rational function method (MGERFM) and the extended sinh-Gordon equation expansion method (shGEEM). The MGERF approach is applied to construct exact solitary wave solutions containing trigonometry, hyperbolic and exponential functions, while the extended shGEE technique is employed to obtain periodic wave solutions containing hyperbolic and Jacobi elliptic functions via performing the symbolic computation in the software package MATHEMATICA. Moreover, by means of standard linear-stability analysis, the modulation instability (MI) and the MI gain spectrum is analytically computed for the considered equation. By selecting suitable parametric values, solution profiles are portrayed in order to make the solutions physically relevant. These results yield periodic waves, kink waves, multi-soliton, and their interactions. By comparing the obtained solutions to the previous findings, we can reveal the novelty of the solutions. In addition, all the obtained solutions were verified by substituting them back into the governing equation using the Mathematica software. The acquired results are significant for the study of wave propagation, signal transmission, and applications of super-transmission phenomena.