Coupled polariton solitons in semiconductor microcavities with a double-well potential

In a double-well microcavity, coupling of spatial polariton solitons between the two wells is studied theoretically. Polaritons trapped inside the double-well structure can demonstrate bistability where both bright and dark polariton solitons are supported. Due to the tunneling effect, the combination of polariton solitons in the two wells can be bright-bright, dark-bright or dark-dark dependent on the initial states (i.e., on-state, off-state, or mixed-state) of the polaritons.     

Soliton Interactions for the Three‐Coupled Discrete Nonlinear Schrödinger Equations in the Alpha Helical Proteins

Three‐coupled discrete nonlinear Schrödinger equations, which describe the dynamics of the three hydrogen bonding spines in the alpha helical proteins with the interspine coupling at the discrete level, are investigated. Binary Bell polynomials are applied to construct the bilinear forms and bilinear Bäcklund transformation of those equations. Propagation characteristics and interactions of the bound‐state solitons are discussed. Bound states of two and three bright solitons arise when all of them propagate in parallel. Elastic interaction between the bound‐state solitons and one bright soliton is given. Increase of the dipole‐dipole interaction energy can lead to the increase of the soliton velocity, that is, the one‐interaction period becomes shorter.     

Instabilities of Multihump Vector Solitons in Coupled Nonlinear Schrödinger Equations

Spectral stability of multihump vector solitons in the Hamiltonian system of coupled nonlinear Schrödinger (NLS) equations is investigated both analytically and numerically. Using the closure theorem for the negative index of the linearized Hamiltonian, we classify all possible bifurcations of unstable eigenvalues in the systems of coupled NLS equations with cubic and saturable nonlinearities. We also determine the eigenvalue spectrum numerically by the shooting method. In case of cubic nonlinearities, all multihump vector solitons in the nonintegrable model are found to be linearly unstable. In case of saturable nonlinearities, stable multihump vector solitons are found in certain parameter regions, and some errors in the literature are corrected.     

Steady bifurcation and solitons in relativistic laser plasmas interaction

In this paper, steady bifurcation and solitons in relativistic laser plasmas interaction are investigated. At first, a new coupled equation for wake wave and the circularly polarized transversal electromagnetic wave is derived. It is a Hamiltonian system with two degrees of freedom. Then, a steady bifurcation analysis based on the coexistence of three different equilibrium states is given. Finally, a condition for predicting the existence of solitons is obtained in terms of the bifurcation control parameter and Hamiltonian function value. The soliton solutions are found numerically. It is shown that the solitons can exist in appropriate regime of vector potential frequency.     

Continuous Families of Embedded Solitons in the Third-Order Nonlinear Schrödinger Equation

The nonlinear Schrödinger equation with a third-order dispersive term is considered. Infinite families of embedded solitons, parameterized by the propagation velocity, are found through a gauge transformation. By applying this transformation, an embedded soliton can acquire any velocity above a certain threshold value. It is also shown that these families of embedded solitons are linearly stable, but nonlinearly semi-stable.     

Micromorphic continuum model for electromagnetoelastic solids

The microcontinuum theory of electroelasticity is considered for polarizable dielectrics on the basis of dipole and quadrupole densities as microfields. Electromagnetic contributions to force, couple, and power are derived, and their correspondence with quantities evaluated in terms of macroscopic polarization and magnetization is examined. A constitutive model that accounts for dissipation is proposed via internal variables satisfying suitable evolution equations. This approach reveals different roles of polarization and strain measures in dissipative processes. The link between the spin inertia tensor and the pair of dipole and quadrupole per unit mass is exploited to derive a nonlinear system of governing equations for a reduced set of variables. The special cases of microstretch and micropolar continua are discussed.     

Vector Solitons and Their Internal Oscilliations in Birefringent Nonlinear Optical Fibers

In this article, the vector solitons in birefringent nonlinear optical fibers are studied first. Special attention is given to the single-hump vector solitons due to evidences that only they are stable. Questions such as the existence, uniqueness, and total number of these solitons are addressed. It is found that the total number of them is continuously infinite and their polarizations can be arbitrary. Next, the internal oscillations of these vector solitons are investigated by the linearization method. Discrete eigenmodes of the linearized equations are identified. Such modes cause to the vector solitons a kind of permanent internal oscillations, which visually appear to be a combination of translational and width oscillations in the A and B pulses. The numerically observed radiation shelf at the tails of interacting pulses is also explained. Finally, the asymptotic states of the perturbed vector solitons are studied within both the linear and nonlinear theory. It is found that the state of internal oscillations of a vector soliton is always unstable. It invariably emits energy radiation and eventually evolves into a single-hump vector soliton state.     

Solitary wave solutions and modulation instability analysis of the nonlinear Schrodinger equation with higher order dispersion and nonlinear terms

We report exact bright and dark solitary wave solution of the nonlinear Schrodinger equation (NLSE) in cubic–quintic non-Kerr medium adopting phase–amplitude ansatz method. We have found the solitary wave parameters along with the constraints under which bright or dark solitons may exist in such a media. Furthermore, we have also studied the modulation instability analysis both in anomalous and normal dispersion regime. The role of fourth order dispersion, cubic–quintic nonlinear parameter and self-steeping parameter on modulation instability gain has been investigated.     

Multi-component vortex solutions in symmetric coupled nonlinear Schrödinger equations

A Hamiltonian system of incoherently coupled nonlinear Schrödinger (NLS) equations is considered in the context of physical experiments in photorefractive crystals and Bose-Einstein condensates. Due to the incoherent coupling, the Hamiltonian system has a group of various symmetries that include symmetries with respect to gauge transformations and polarization rotations. We show that the group of rotational symmetries generates a large family of vortex solutions that generalize scalar vortices, vortex pairs with either double or hidden charge, and coupled states between solitons and vortices. Novel families of vortices with different frequencies and vortices with different charges at the same component are constructed and their linearized stability problem is block-diagonalized for numerical analysis of unstable eigenvalues.     

General N‐Dark–Dark Solitons in the Coupled Nonlinear Schrödinger Equations

N‐dark–dark solitons in the integrable coupled NLS equations are derived by the KP‐hierarchy reduction method. These solitons exist when nonlinearities are all defocusing, or both focusing and defocusing nonlinearities are mixed. When these solitons collide with each other, energies in both components of the solitons completely transmit through. This behavior contrasts collisions of bright–bright solitons in similar systems, where polarization rotation and soliton reflection can take place. It is also shown that in the mixed‐nonlinearity case, two dark–dark solitons can form a stationary bound state.     

Stiff Oscillatory Systems, Delta Jumps and White Noise

Two model problems for stiff oscillatory systems are introduced. Both comprise a linear superposition of harmonic oscillators used as a forcing term for a scalar ODE. In the first case the initial conditions are chosen so that the forcing term approximates a delta function as and in the second case so that it approximates white noise. In both cases the fastest natural frequency of the oscillators is <e6>OM</e6>(N). The model problems are integrated numerically in the stiff regime where the time-step satisfies The convergence of the algorithms is studied in this case in the limit and For the white noise problem both strong and weak convergence are considered. Order reduction phenomena are observed numerically and proved theoretically. August 25, 1999. Final version received: May 3, 2000.     

Soliton experiments in transmission lines

Different structures of the nonlinear electrical transmission lines are presented, including coupled, inhomogeneous and two-dimensional lines, and the all basic soliton phenomena, such as the formation of solitons from the initial state, the recurrence of solitons, the envelope solitons, and a.c.-driven solitons, which are observed using transmission lines, are demonstrated.     

Quantum solitons and the Haldane phase in antiferromagnetic spin chains

A survey is given of the relevance of solitons for the present understanding of antiferromagnetic quantum spin chains. For the -chain the basic elementary excitations are solitons. Two solitons combine to form a magnon and its internal degree of freedom is observed as an excitation continuum. For S = 1 chains the existence of the massive Haldane phase is related to the dissociation of soliton pairs (pairs of domain walls with respect to antiferromagnetic order). Based on the hidden (or string) order, the appropriate mean field theory for antiferromagnetic S = 1 chains is introduced as based on uncorrelated solitons and applied to calculate correlation functions. It is described how to include correlations between solitons using an approximate mapping to an effective chain. The basic elementary excitations in the Haldane phase are identified as solitons with respect to the hidden order.     

Two-dimensional magnetic solitons and thermodynamics of quasi-two-dimensional magnets

The article reviews two-dimensional magnetic solitons in a classical weakly-anisotropic Heisenberg magnets. Topological classification, structure, dynamical properties and thermodynamical contribution of 2D solitons to response functions of the magnet are discussed. Based on effective equations of motion we calculated the soliton contribution to the dynamical structure factor of ferromagnets and antiferromagnets both for localized topological solitons and magnetic vortices.     

Variable sinh-Gaussian solitons in nonlocal nonlinear Schrödinger equation

Based on the nonlocal nonlinear Schrödinger equation that governs phenomenologically the propagation of laser beams in nonlocal nonlinear media, we theoretically investigate the propagation of sinh-Gaussian beams (ShGBs). Mathematical expressions are derived to describe the beam propagation, the intensity distribution, the beam width, and the beam curvature radius of ShGBs. It is found that the propagation behavior of ShGBs is variable and closely related to the parameter of sinh function (PShF). If the PShF is small, the transverse pattern of ShGBs keeps invariant during propagation for a proper input power, which can be regarded as solitons. If the PShF is large, it varies periodically, which is similar to the evolution of temporal higher-order solitons in nonlinear optical fiber. Numerical simulations are carried out to illustrate the typical propagation characteristics.     

Trapped instability and vortex formation by an unstable coastal current

This paper addresses the instability of a two-layer coastal current in a quasigeostrophic model; the potential vorticity (PV) structure of this current consists in two uniform cores, located at different depths, with finite width and horizontally shifted. This shift allows both barotropic and baroclinic instability for this current. The PV cores can be like-signed or opposite-signed, leading to their vertical alignment or to their hetonic coupling. These two aspects are novel compared to previous studies. For narrow vorticity cores, short waves dominate, associated with barotropic instability; for wider cores, longer waves are more unstable and are associated with baroclinic processes. Numerical experiments were performed on the f-plane with a finite-difference model. When both cores have like-signed PV, trapped instability develops during the nonlinear evolution: vertical alignment of the structures is observed. For narrow cores, short wave breaking occurs close to the coast; for wider cores, substantial turbulence results from the entrainment of ambient fluid into the coastal jet. When the two cores have opposite-signed PV, the nonlinear regimes range from short wave breaking to the ejection of dipoles or tripoles, via a regime of dipole oscillation near the wall. The Fourier analysis of the perturbed flow is appropriate to distinguish the regimes of short wave breaking, of dipole formation, and of turbulence, but not the differences between regimes involving only vortex pairs. To explain more precisely the regimes where two vortices (and their wall images) interact, a point vortex model is appropriate.     

Maximum principles and gradient Ricci solitons

It is shown that the Omori-Yau maximum principle holds true on complete gradient shrinking Ricci solitons both for the Laplacian and the f-Laplacian. As an application, curvature estimates and rigidity results for shrinking Ricci solitons are obtained. Furthermore, applications of maximum principles are also given in the steady and expanding situations.     

Application and analysis of direct sampling method in real-world microwave imaging

In this paper, a direct sampling method (DSM) is designed for a real-time detection of small anomalies from scattering parameters measured by a small number of dipole antennas. Applicability of the DSM is theoretically demonstrated by proving that its indicator function can be represented in terms of an infinite series of Bessel functions of integer order, Hankel function of order zero, and the antenna configurations. Experiments using real-data then demonstrate both the effectiveness and limitations of this method.