Spectral incoherent solitons: a localized soliton behavior in the frequency domain

We show both theoretically and experimentally in an optical fiber system that a noninstantaneous nonlinear environment supports the existence of spectral incoherent solitons. Contrary to conventional solitons, spectral incoherent solitons do not exhibit a confinement in the spatiotemporal domain, but exclusively in the frequency domain. The theory reveals that the causality condition inherent to the nonlinear response function is the key property underlying the existence of spectral incoherent solitons. These solitons constitute nonequilibrium stable states of the incoherent field and are shown to be robust with respect to binary collisions.     

Exact solutions for bright and dark solitons in spatially inhomogeneous nonlinearity

We present exact analytical results for bright and dark solitons in a type of one-dimensional spatially inhomogeneous nonlinearity. We show that the competition between a homogeneous self-defocusing (SDF) nonlinearity and a localized self-focusing (SF) nonlinearity supports stable fundamental bright solitons. For a specific choice of the nonlinear parameters, exact analytical solutions for fundamental bright solitons have been obtained. By applying both variational approximation and Vakhitov-Kolokolov stability criterion, it is found that exact fundamental bright solitons are stable. Our analytical results are also confirmed numerically. Additionally, we show that a homogeneous SF nonlinearity modulated by a localized SF nonlinearity allows the existence of exact dark solitons, for certain special cases of nonlinear parameters. By making use of linear stability analysis and direct numerical simulation, it is found that these exact dark solitons are linearly unstable.     

线性聚焦和线性散焦效应对空间光孤子间相互作用的影响

考虑非均匀一维自聚焦介质的横向不均匀性,利用非线性薛定谔方程满足的守恒律给出了相邻空间孤子间隔的解析式,并对空间孤子之间的相互作用进行了数值模拟.结果表明,线形聚焦效应增强了空间孤子之间的相互作用;而线形散焦效应减弱了空间孤子之间的相互作用.当不考虑介质横向不均匀时,空间孤子之间发生周期性的碰撞.线性散焦效应使相邻空间孤子之间的间隔随传输距离发生周期性的变化,但孤子之间并不发生碰撞.线性聚焦效应使相邻空间孤子随传输距离发生周期性的碰撞,线性聚焦效应具有压制损耗使相邻空间孤子间隔变大的作用.     

Stable spinning optical solitons in three dimensions

We introduce spatiotemporal spinning solitons (vortex tori) of the three-dimensional nonlinear Schr?dinger equation with focusing cubic and defocusing quintic nonlinearities. The first ever found completely stable spatiotemporal vortex solitons are demonstrated. A general conclusion is that stable spinning solitons are possible as a result of competition between focusing and defocusing nonlinearities.     

Three-dimensional spatiotemporal solitary waves in strongly nonlocal media

We construct a class of three-dimensional strongly nonlocal spatiotemporal solitary waves of the nonlocal nonlinear Schrödinger equation, by using superpositions of single accessible solitons as initial conditions. Evolution of such solitary waves, termed the accessible light bullets, is studied numerically by choosing specific values of topological charges and other solitonic parameters. Our numerical results reveal that in strongly nonlocal nonlinear media with a Gaussian response function, different classes of accessible spatiotemporal solitons can be generated and controlled by tailoring different soliton parameters.     

Controlling soliton explosions

We investigate the dynamics of solitons in generalized Klein–Gordon equations in the presence of nonlinear damping and spatiotemporal perturbations. We will present different mechanisms for soliton explosions. We show (both analytically and numerically) that some space-dependent perturbations or nonlinear damping can make the soliton internal mode unstable leading to soliton explosion. We will show that, in some cases, while some conditions are satisfied, the soliton explodes becoming a permanent, extremely complex, spatiotemporal dynamics. We believe these mechanisms can explain some of the phenomena that recently have been reported to occur in excitable media. We present a method for controlling soliton explosions.     

Transport of Nonautonomous Solitons in Two‐Dimensional Disordered Media

Transport of localized nonlinear excitations in disordered media is an interesting and important topic in modern physics. Investigated in this work is transport of two‐dimensional (2D) solitons for a nonlinear Schrödinger equation with inhomogeneous nonlocality and disorder. We use the variational method to show that, the shape (size) of solitons can be manipulated through adjusting the nonlocality, which, in turn, affects the soliton mobility. Direct numerical simulations reveal that the influence of disorder on the soliton transport accords with our analysis by the variational method. Besides, we have demonstrated an anisotropic transport of the 2D nonautonomous solitons as well. Our study is expected to shed light on modulating solitons through material properties for specifying their transport in disordered media.     

PROPAGATION OF TWIST SOLITONS IN FULLY INHOMOGENEOUS DNA CHAINS

In the framework of a recently introduced model of DNA torsional dynamics, we argued — on the basis of perturbative considerations — that an inhomogeneous DNA chain could support long-lived soliton-type excitations due to the peculiar geometric structure of DNA and the effect of this on nonlinear torsional dynamics. Here we consider an inhomogeneous version of this model of DNA torsional dynamics, and investigate numerically the propagation of solitons in a DNA chain with a real base sequence (corresponding to the Human Adenovirus 2); this implies inhomogeneities of up to 50% in the base masses and inter-pair interactions. We find that twist solitons propagate for considerable distances (2–10 times their diameters) before stopping due to phonon emission. Our results show that twist solitons may exist in realistic DNA chain models, and on a more general level that solitonic propagation can take place in highly inhomogeneous media. The most relevant feature for general nonlinear dynamics is that we identify the physical mechanisms allowing this behavior and thus the class of models candidate to support long-lived soliton-type excitations in the presence of significant inhomogeneities.     

Collisions of Two Spatial Solitons in Inhomogeneous Nonlinear Media

Collisions of spatial solitons occurring in the nonlinear Schröinger equation with harmonic potential are studied, using conservation laws and the split-step Fourier method. We find an analytical solution for the separation distance between the spatial solitons in an inhomogeneous nonlinear medium when the light beam is self-trapped in the transverse dimension. In the self-focusing nonlinear media the spatial solitons can be transmitted stably, and the interaction between spatial solitons is enhanced due to the linear focusing effect (and also diminished for the linear defocusing effect). In the self-defocusing nonlinear media, in the absence of self-trapping or in the presence of linear self-defocusing, no transmission of stable spatial solitons is possible. However, in such media the linear focusing effect can be exactly compensated, and the spatial solitons can propagate through.     

Lie symmetries and solitons in nonlinear systems with spatially inhomogeneous nonlinearities

Using Lie group theory and canonical transformations, we construct explicit solutions of nonlinear Schr?dinger equations with spatially inhomogeneous nonlinearities. We present the general theory, use it to show that localized nonlinearities can support bound states with an arbitrary number solitons, and discuss other applications of interest to the field of nonlinear matter waves.     

Accessible solitons in three-dimensional parabolic cylindrical coordinates

A class of self-similar beams, named three-dimensional (3D) spatiotemporal parabolic accessible solitons, are introduced in the 3D highly nonlocal nonlinear media. We obtain exact solutions of the 3D spatiotemporal linear Schrödinger equation in parabolic cylindrical coordinates by using the method of separation of variables. The 3D localized structures are constructed with the help of the confluent hypergeometric Tricomi functions and the Hermite polynomials. Based on such an exact solution, we graphically display three different types of 3D beams: the Gaussian solitons, the ring necklace solitons, and the parabolic solitons, by choosing different mode parameters. We also perform direct numerical simulation to discuss the stability of local solutions. The procedure we follow provides a new method for the manipulation of spatiotemporal solitons.     

Nonautonomous Solitons in the(3+1)-Dimensional Inhomogeneous Cubic-Quintic Nonlinear Medium

We have constructed explicit nonautonomous soliton solutions of the generalized nonlinear Schrdinger equation in the(3+1)-dimensional inhomogeneous cubic-quintic nonlinear medium.The gain parameter has no effects on the motion of the soliton's phase or their velocities,and it affects just the evolution of their peaks.As two examples,we discuss the propagation of nonautonomous solitons in the periodic distributed amplification system and the exponential dispersion decreasing system.Results show that the presence of the chirp not only makes the intensity of solitons weaken more promptly,but also broadens their width.     

Spatiotemporal discrete Ginzburg-Landau solitons in two-dimensional photonic lattices

In the framework of the continuous-discrete cubic-quintic Ginzburg-Landau model, spatiotemporal dissipative solitons which are highly confined inside two-dimensional photonic lattices are found numerically. The domains of existence in the relevant parameter space, of in-phase (unstaggered) on-site (single-peaked), inter-site (double-peaked), and flat-top-like (four-peaked) spatiotemporal dissipative solitons are determined. We show that the on-site solitons are stable in the whole domain of their existence and we find the stability domains of both inter-site and flat-top-like solitons. We describe the complex instability-induced scenarios of the dynamics of spatiotemporal discrete Ginzburg-Landau solitons in two-dimensional photonic lattices.     

Dissipative Vortex Solitons in Defocusing Media with Spatially Inhomogeneous Nonlinear Absorption

In this paper, by solving a complex nonlinear Schr¨odinger equation, radially symmetric dissipative vortex solitons are obtained analytically and are tested numerically. We find that spatially inhomogeneous nonlinear absorption gives rise to the stability of dissipative vortex solitons in self-defocusing nonlinear medium in the presence of constant linear gain. Numerical simulation reveals the interaction effect among linear gain and nonlinear loss in the azimuthal modulation instabilities of these vortices suppression. Apart from the uniform linear gain indeed affects the stability of vortex in this media, another noticeable feature of current setup is that the steep spatial modulation of the nonlinear absorption can suppress sidelobes effectively and support stable vortex solitons in situations with uniform linear gain.Under appropriate conditions, the vortex solitons can propagate stably and feature no symmetry breaking, although the beams exhibit radical compression and amplification as they propagate.     

Localized nonlinear waves in combined time-dependent magnetic–optical potentials with spatiotemporally modulated nonlinearities

We construct explicit novel solutions of the nonlinear Schrödinger equation with spatiotemporal modulation of the nonlinearities and potentials. By using a modified similarity transformation we explore some localized nonlinearities and combined time-dependent magnetic–optical potentials in the form of linear-lattice ones and harmonic-lattice ones. Several families of exact localized nonlinear wave solutions in terms of Mathieu and elliptic functions corresponding to these potentials are then studied, such as snakelike solitons and breathing solitons. The stability of the obtained localized nonlinear wave solutions is investigated numerically such that some stable solutions are found.     

Algebraic bright and vortex solitons in defocusing media

We demonstrate that spatially inhomogeneous defocusing nonlinear landscapes with the nonlinearity coefficient growing toward the periphery as (1+|r|(α)) support one- and two-dimensional fundamental and higher-order bright solitons, as well as vortex solitons, with algebraically decaying tails. The energy flow of the solitons converges as long as nonlinearity growth rate exceeds the dimensionality, i.e., α>D. Fundamental solitons are always stable, while multipoles and vortices are stable if the nonlinearity growth rate is large enough.     

Intensity redistribution and shape changing collision in coupled femtosecond solitons

In this paper, we investigate the two coupled higherorder inhomogeneous nonlinear Schrödinger equationusing gauge transformation approach and generate femtosecondsoliton solutions for the two modes. We then show how theintensities of the solitons can redistribute among the modesleading to fascinating shape changing collision of femtosecondsolitons. We also observe that the above integrable model isendowed with a rare freedom which offers the possibility ofinjecting electromagnetic energy into the pulses through fibreparameters facilitating femtosecond soliton management.     

Spatial solitons in an optical lattice with varying diffraction and spatially inhomogeneous nonlinearity

In this paper, we present the (1+1)-dimensional inhomogeneous nonlinear Schrödinger (NLS) equation that describes the propagation of optical waves in nonlinear optical systems exhibiting optical lattice, inhomogeneous nonlinearity and varying diffraction at the same time. A series of interesting properties of spatial solitons are found from the numerical calculations, such as the stable propagation in the a nonperiodic optical lattice induced by periodic diffraction variations and periodic nonlinearity variations. Finally, the interaction of neighboring spatial solitons in a nonperiodic optical lattice is discussed, and the results reveal that two spatial solitons can propagate periodically and separately in the optical lattice without interaction.     

Nonlinear theory of transverse perturbations of quasi-one-dimensional solitons

An averaged variational principle is applied to analyze the nonlinear effect of transverse perturbations (including diffraction) on quasi-one-dimensional soliton propagation governed by various wave equations. It is shown that parameters of the spatiotemporal solitons described by the cubic Schrödinger equation and the Yajima-Oikawa model of interaction between long-and short-wavelength waves satisfy the spatial quintic nonlinear Schrödinger equation for a complex-valued function composed of the amplitude and eikonal of the soliton. Three-dimensional solutions are found for two-component “bullets” having long-and short-wavelength components. Vortex and hole-vortex structures are found for envelope solitons and for two-component solitons in the regime of resonant long/short-wave coupling. Weakly nonlinear behavior of transverse perturbations of one-dimensional soliton solutions in a self-defocusing medium is described by the Kadomtsev-Petviashvili equation. The corresponding rationally localized “lump” solutions can be considered as secondary solitons propagating along the phase fronts of the primary solitons. This conclusion holds for primary solitons described by a broad class of nonlinear wave equations.     

Gap solitons in an extended anti-directional coupler

A nonlinear solitary wave in an inhomogeneous medium formed by two tunnel-coupled waveguides is considered. One of the waveguides is manufactured from an ordinary dielectric, while the second has negative refraction. The results from numerical simulations demonstrate the high stability of gap solitons with respect to collisions. It is discovered that for low relative velocities of two colliding solitons, a longlived coupled state of these solitons can be formed.