Solitons In Media Research Articles

Elliptical and rectangular solitons in media with competing cubic–quintic nonlinearities

We demonstrate two new types of non-circularly-symmetric solitons, the elliptical and rectangular solitons, which can be sustained by the cubic–quintic nonlinearity in the nonlinear Schrödinger equation with a linear potential well. The characteristics of these solitons are investigated in some detail. Notably, the elliptical and circular solitons can transform into each other, and similarly the rectangular and square solitons can transform into each other. Interestingly, we find that elliptical and rectangular solitons can also transform into each other—a phenomenon not readily seen among different types of solitons. In addition, the rotation of elliptical and rectangular solitons is displayed as well. Finally, we find that stable vortex modes of elliptical and rectangular solitons can be also supported by our model.

Exploring dynamic behaviors of soliton-like pulses in the lossy electrical transmission line model with fractional derivatives: A comparative study

This study aims to explore the intricate behavior of soliton-like pulses within a nonlinear and lossy electrical transmission line. The transmission line is described by a mathematical model called the “beta derivative”, which is specifically designed to characterize the propagation of electrical solitons in media with both nonlinearity and dispersion properties. To achieve this goal, the (G′/G2)-expansion method is applied to a periodically loaded nonlinear beta derivative lossy transmission line with symmetric voltage-dependent capacitances. Soliton-like pulses, including periodic singular, dark, bright, and singular waves, are obtained using the (G′/G2)-expansion method based on the voltage equation. Three-dimensional and two-dimensional graphs of some of the obtained novel solutions satisfying relevant equations are provided to understand the underlying mechanisms of the soliton family. In terms of fractionality, the profiles of dark or bright waveforms maintain their complete forms, but their smoothness increases as the fractional parameters increase. On the other hand, periodic wave solutions exhibit an increase in periodicity. By adjusting the parameters of the model, the characteristics of the waves can be modified to generate desired wave profiles. Additionally, the study involves a comprehensive comparison among solutions derived from models incorporating the beta, conformable, and M−truncated derivatives. It examines how the amplitude of the solitons is influenced by the fractional parameter, utilizing graphs to visualize this impact by assigning specific fractional parameter values. These pulse-like solitons offer promising potential for integration within telecommunication systems, where they can function as information carriers, facilitating heightened data bit rates. By leveraging the findings of this study, advancements in telecommunication technology can be pursued, leading to enhanced efficiency and improved performance.

Stable fundamental two-dimensional solitons in media with competing nonlocal interactions

Soliton attract a great deal of attention across various disciplines, from optics to fluid mechanics, cosmology, as well as particle and condensed matter physics, due to their unique characteristics and applications. Although various soliton solutions are known, it is rare to find stable fundamental bright solitons with complex amplitude structures in two transverse dimensions. Here we show that the interplay between nonlocal nonlinear light–matter attraction and repulsion can lead to novel types of solutions in two spatial dimensions. We find unusual new fundamental soliton solutions exhibiting complex intensity but constant phase profiles with rectangular and cylindrical symmetries. We also employ an analytically tractable novel model for a complex linear potential whose two-peak ground states mimic two-peak solitons.

Management of solitons in medium with competing cubic and quadratic nonlinearities

Management of solitons in media with competing quadratic and cubic nonlinearities is investigated. Two schemes, using rapid modulations of a mismatch parameter, and of the Kerr nonlinearity parameter are studied. For both cases, the averaged in time wave equations are derived. In the case of mismatch management, the region of the parameters where stabilization is possible is found. In the case of Kerr nonlinearity management, it is shown that the effective χ(2) nonlinearity depends on the intensity imbalance between fundamental (FH) and second (SH) harmonics. Predictions obtained from the averaged equations are confirmed by numerical simulations of the full PDE’s.

Solitons in media with mixed, high-order dispersion and cubic nonlinearity

Although most soliton research has traditionally considered dominant quadratic dispersion, the recent discovery of pure-quartic solitons has inspired analysis of soliton solutions with large higher orders of dispersion. Here we present analytic expressions for families of bright soliton solutions at arbitrary dispersion orders and practical methods to obtain the associated dispersion relations. These results provide a framework for considering higher order dispersion solitons and show the potential for further investigation of solitons in higher order dispersion systems.

Effects of Lattice Frequency on Vacancy Defect Solitons in a Medium with Quadratic Nonlinear Response

The impact of lattice frequency on the defect lattice solitons have been investigated in a medium with quadratic nonlinear response. Governing equation of the optical system has been formed by adding an external lattice to the NLSM system, and soliton solutions of the system were calculated by the squared operator method. Moreover, stability of the fundamental solitons have been examined by the linear stability spectra and nonlinear evolution of the solitons. It has been demonstrated that although higher lattice frequency extends the existence domain of defective lattice solitons in a quadratic nonlinear medium, it negatively effects the stability dynamics of the solitons.

Tubular topological bright-dark and dark laser solitons

We investigate, analytically and numerically, tubular topological laser solitons, which serve as intermediate link between 2D- and 3D-dissipative optical solitons in media with nonlinear amplification and absorption of light or in large-size laser with such a medium. Features of both 3D-dark solitons (with nonvanishing intensity at periphery for all spatial dimensions) and bright-dark solitons (vanishing in two of three dimensions) are studied, including their stability.

Soliton dynamics in finite nonlocal media with cylindrical symmetry

The effect of finite boundaries in the propagation of spatial nonlocal solitons in media with cylindrical symmetry is analyzed. Using Ehrenfest's theorem together with the Green's function of the nonlinear refractive index equation, we derive an analytical expression for the force exerted on the soliton by the boundaries, verifying its validity by full numerical propagation. We show that the dynamics of the soliton are determined not only by the degree of nonlocality, but also by the boundary conditions for the refractive index. In particular, we report that a supercritical pitchfork bifurcation appears when the boundary condition exceed a certain threshold value.

Generation of solitons in media with arbitrary degree of nonlocality using an optimization procedure

Using a recently developed technique based on the Rayleigh-Ritz optimization principle, we generate solitons for media with an arbitrary degree of nonlocality. We demonstrate that it is possible to obtain a plethora of complex self-trapped beams using known solutions to the harmonic oscillator for one-dimensional (1D), 2D, and 3D systems, but working directly with a generalized nonlinear nonlocal Schr\odinger equation. We compare the parameters obtained variationally between the phenomenological Gaussian response and other more realistic nonlocal responses. We report that, for both kinds of nonlocal models, our approach obtains variational solutions that can remain self-trapped for certain conditions. We corroborate that, in general, the soliton dynamics can be different between the Gaussian response and the more realistic media for an arbitrary degree of nonlocality.

Gauss-type solitons of (1+1)-dimensional cubic-quintic-septimal nonlinear Schrödinger equation with Gauss-type [formula omitted]-symmetric potentials

The Gauss-type PT-symmetric potentials acting on cubic-quintic-septimal nonlinear media are studied, and two kinds of Gauss-type solitons in these media are analytically derived. The comparison of form characteristics between two kinds of Gauss-type solitons is discussed, including the real part, imaginary part and intensity of Gauss-type solitons. Moreover, based on the eigenvalue method, the linear stability analysis for solutions is given, and then utilizing numerical simulation with the split-step Fourier method, the stability of Gauss-type solitons in different nonlinear media is further checked.

Optical solitons in media with focusing and defocusing saturable nonlinearity and a parity-time-symmetric external potential.

We report results for solitons in models of waveguides with focusing or defocusing saturable nonlinearity and a parity-time ([Formula: see text])-symmetric complex-valued external potential of the Scarf-II type. The model applies to the nonlinear wave propagation in graded-index optical waveguides with balanced gain and loss. We find both fundamental and multipole solitons for both focusing and defocusing signs of the saturable nonlinearity in such [Formula: see text]-symmetric waveguides. The dependence of the propagation constant on the soliton's power is presented for different strengths of the nonlinearity saturation, S The stability of fundamental, dipole, tripole and quadrupole solitons is investigated by means of the linear-stability analysis and direct numerical simulations of the corresponding (1+1)-dimensional nonlinear Schrödinger-type equation. The results show that the instability of the stationary solutions can be mitigated or completely suppressed, increasing the value of SThis article is part of the theme issue 'Dissipative structures in matter out of equilibrium: from chemistry, photonics and biology (part 1)'.

Mean-Frequency Shift of the Envelope Solitons in Media with Cubic Relaxing Nonlinearities

We study the mean-frequency variation of the envelope solitons propagating in nonlinear media with relaxing cubic nonlinearities. It is shown that the mean frequency in the propagation cannot only decrease in the case of the positive nonlinearity coefficient, which was previously known, but also increase in the case of the negative nonlinearity coefficient, which is observed for the gravity waves on a liquid surface.

Beta-derivative and sub-equation method applied to the optical solitons in medium with parabolic law nonlinearity and higher order dispersion

By using the sub-equation method, we construct the analytical solutions of the space-time generalized nonlinear Schrödinger equation involving the beta-derivative. This equation describing the propagation of ultra-short optical solitons through parabolic law medium. Nonlinear perturbations of higher-order and self-steepening terms are taken into account. As a result, some new exact solutions are constructed under constraint conditions.

High-frequency solitons in media with induced scattering from damped low-frequency waves with nonuniform dispersion and nonlinearity

The dynamics of high-frequency field solitons is considered using the extended nonhomogeneous nonlinear Schrodinger equation with induced scattering from damped low-frequency waves (pseudoinduced scattering). This scattering is a 3D analog of the stimulated Raman scattering from temporal spatially homogeneous damped low-frequency modes, which is well known in optics. Spatial inhomogeneities of secondorder linear dispersion and cubic nonlinearity are also taken into account. It is shown that the shift in the 3D spectrum of soliton wavenumbers toward the short-wavelength region is due to nonlinearity increasing in coordinate and to decreasing dispersion. Analytic results are confirmed by numerical calculations.

Terahertz solitons

This paper presents a theoretical study of soliton and solitonlike propagation regimes of broad-band terahertz pulses in nonlinear crystals. The standard approximation of slowly varying amplitudes for quasi-monochromatic signals is not used in this case. Solitonlike propagation regimes known in other areas of physics and those unknown earlier are analyzed. Solitons in media that contain tunnel quantum transitions are studied in detail.

The surface solitons in media with uniform and Gaussian modulated potentials

We investigate the existence and stability of solitons in media with uniform and Gaussian modulated potentials, including linear case, and self-focusing and self-defocusing nonlinear cases. For linear case, the eigenvalues and eigenfunction for different modulated depths of Gaussian potentials are obtained numerically. For nonlinear cases, the existence and stability of fundamental and multipole solitons are studied in self-focusing and self-defocusing media. For a fixed modulated depth, the eigenvalue for fundamental or multipole linear modes is equal to the critical propagation constant bc of fundamental and multipole solitons existence. Fundamental solitons are stable in both the self-defocusing nonlinear media and the self-focusing nonlinear case. Multipole solitons are stable with the propagation constants close to bc both for self-focusing and self-defocusing nonlinearities.

Stability conditions for one-dimensional optical solitons in cubic-quintic-septimal media

Conditions for stable propagation of one-dimensional bright spatial solitons in media exhibiting optical nonlinearities up to the seventh-order are investigated. The results show well-defined stability regions even when all the nonlinear terms are focusing. Conditions for onset of the supercritical collapse of the optical beam are identified too. A variational approximation is used to predict dependence of the soliton propagation constant on the norm, and respective stability regions are identified using the Vakhitov-Kolokolov criterion. Analytical results obtained by means of the variational approximation are corroborated by numerical simulations of the cubic-quintic-septimal nonlinear Schroedinger equation.

Optical solitons in media with time-modulated nonlinearities and spatiotemporal dispersion

This work studies the optical solitons with time-modulated nonlinearities and spatiotemporal dispersion. Four types of nonlinearity—Kerr law nonlinearity, parabolic law nonlinearity, power law nonlinearity, and dual-power law nonlinearity—are considered. The non-auto-Backlund transformation is obtained. Analytical soliton solutions are constructed. The presented results can be applied in the area of dispersion- and nonlinearity-managed solitons.

Two-dimensional solitons in a quintic-septimal medium

We report an observation of spatial solitons in a medium managed to present fifth-seventh (focusing-defocusing) refractive nonlinearities with suppressed third-order nonlinearity. Propagation of two-dimensional bright spatial solitons for \ensuremath{\sim}10 Rayleigh lengths was observed and characterized in a suspension of silver nanoparticles in acetone using the scattered light imaging method. Numerical calculations based on a nonlinear Schr\odinger-type equation, including contributions up to the seventh-order susceptibility, were performed showing good agreement with the experimental results.

Optical solitons in medium with parabolic law nonlinearity and higher order dispersion

The nonlinear Schrödinger equation, describing the propagation of ultra-short optical solitons through parabolic law medium, has been studied analytically. The perturbations that are third-order dispersion, fourth-order dispersion, and self-steepening are taken into account. The Ricatti equation expansion approach and Ansatz method are applied. Finally, Bright, dark as well as singular solitons are constructed under some constraint conditions.