We find and analyze analytically and numerically two new families of coupled soliton states in nonlinear fiber couplers. The bifurcation diagram for the new types of soliton states is constructed. It is shown that the bifurcation diagram for the fiber coupler is similar to the bifurcation diagram for the stationary waves in a symmetric nonlinear planar waveguide. Physical reasons for this analogy are discussed.

We report experimental results for convection in a thin horizontal layer of a fluid which is heated from below and which undergoes a first-order phase change. For some parameter ranges the denser layer may be stably stratified above the lighter one, as predicted by Busse and Schubert. Over various parameter ranges we observed hexagonal, inverted-hexagonal, and roll flow. Interesting interactions between two-phase convection and Rayleigh-Bénard convection are observed near two codimension-two points.

We report the first observation of a spectral resonance in the lateral displacement (Goos-Hänchen shift) of a laser beam totally reflected from a glass-cesium vapor interface. The line shape and the magnitude of the effect are well described by a model taking atom-wall collisions into account.

We propose a scheme for producing a spatial and temporal averaged gain of 45 ${\mathrm{cm}}^{\mathrm{-}1}$ in nickel-like Ta, including refraction. This result is achieved by irradiating a 40 μg/${\mathrm{cm}}^2$ target with a low intensity pulse [2ω(λ=0.53 μm), 5×${10}^{13}$ W/${\mathrm{cm}}^2$, 80 ps] to make the plasma subcritical. This is followed by a high intensity pulse (2ω, 2×${10}^{15}$, 20 ps) to give the proper ionization. Therefore the principle of pulse shaping to achieve high gain using high intensity pump radiation is demonstrated.

Periodic two-dimensional waves on the surface of a flowing film are generally unstable. We have investigated their breakdown experimentally to determine the process by which film flows undergo a transition to spatiotemporal chaos. The two-dimensional secondary instabilities studied here are convective (like the primary instability); both subharmonic and sideband instabilities occur, but in different ranges of frequency.

The effects of internal noise on chaotic and periodic dynamics of a chemical system are investigated. Calculations are carried out for a mesoscopic model of the Williamowski-Rössler reaction, a mass-action model that displays deterministic chemical chaos. The model incorporates internal fluctuations that arise from the reactive and diffusion processes in the system. The character of noisy dynamics is analyzed and questions related to the validity of deterministic models in the chaotic regime are discussed. The interplay among spatial degrees of freedom, system size, and internal fluctuations are studied for this chaotic dynamical system.

The destruction of quantum localization of chaos by weak nonlinearity is analyzed on the basis of the Chirikov criterion of overlapping resonances. It is shown that for the nonlinear coupling constant there is a delocalization border above which localization is destroyed. In this delocalized phase, excitation is described by a universal anomalous subdiffusion law. Applications of this phenomenon to nonlinear wave propagation in disordered media and Anderson localization are discussed.

We present the results of an experimental study of a supercritical parity-breaking transition in the printer’s instability. Above the transition, the reflection symmetry of a one-dimensional pattern of stationary fingers is broken and the pattern propagates at constant speed. We find the speed of the broken-parity pattern to be proportional to the degree of a symmetry of the pattern, and the wave number to decrease linearly with the asymmetry.

It is demonstrated theoretically that the critical Rayleigh number for transition from the no-motion (conduction) to the motion state in the Rayleigh-Bénard problem of an infinite fluid layer heated from below and cooled from above can be significantly increased through the use of feedback control strategies effecting small perturbations in the boundary data.

The energy spectrum for a tight binding model with on-site potentials forming a Cantor set is seen to have a globally self-similar structure, and an exact correlation of the wave functions with the energies is pointed out. With periodic driving the quasienergy spectrum is obtained from an equivalent lattice problem and is seen to imply nonrecurrent time evolution of states. A model system with a discrete spectrum shows similar behavior. Implications for the problem of microwave ionization of hydrogen atoms are indicated.

Recently, ultranarrow resonances have been observed in the diamagnetic Rydberg spectrum of the lithium atom. We show that they originate from an accidental destructive interference, which, in turn, is due to the chaotic character of the classical behavior. Our numerical simulations show that their statistical properties are well described by a random-matrix model.

It is shown that a gas composed of inelastically colliding particles is unstable to the formation of high density clusters. A possible physical mechanism underlying this instability is proposed. A theoretical analysis, based on the Jenkins-Richman equations, as well as a numerical simulation of the dynamics of an unforced system of hard disks in a periodic rectangular enclosure, renders support to the proposed mechanism. In particular, a simple formula for the characteristic intercluster distance is derived and found to be in agreement with the numerical results. Applications to granular systems of engineering interest as well as to astrophysics are briefly outlined.

It has been a long-standing problem to understand the eigenfunctions of a system whose classical analog is strongly chaotic. We show that in some cases the eigenfunctions can be constructed by purely semiclassical calculations.

It is demonstrated that scattering by a rough surface can be described in terms of the coherent transfer function, which was first developed to describe the process of imaging. The two-dimensional (one transverse and one longitudinal) coherent transfer function for confocal imaging is presented for a high-angle theory. From this an effective transfer function for imaging of rough surfaces is developed, based on the Kirchhoff approximation. It is described how confocal imaging can be used to investigate various scattering mechanisms, and can be used for reconstruction of surface profiles in the Kirchhoff approximation.

The spontaneous Raman effect in ${\mathrm{C}}_6$${\mathrm{H}}_6$ is investigated in the QED-vacuum confinement condition in the Casimir topology of an optical microcavity as a prototype inelastic quantum-scattering process at optical frequencies. The confinement determines a dramatic enhancement (over a factor of ${10}^3$), inhibition, and directional effects on the scattering intensity. Apart from its relevance in atomic and molecular spectroscopy, the work establishes a new perspective in the field of QED scattering involving quantum particles with any energy.

We show how the generation of vacuum uv radiation can be doubly- enhanced by using strong external electromagnetic fields so that one can simultaneously make use of (a) the amplification of the fundamental as it propagates through the medium and (b) the near-zero absorption of the generated vacuum uv radiation. We include in the analysis the effects of propagation and pump depletion.

We include the effect of density-dependent near dipole-dipole interactions in order to generalize the theory of a simple three-level system that exhibits lasing without inversion and an enhanced index of refraction at zero absorption. For certain values of atomic density, our generalized theory predicts a novel enhancement of inversionless gain and absorptionless index by more than 2 orders of magnitude.

Phase and amplitude dynamics of a subcritical period-doubling bifurcation are experimentally characterized in the nonlinear strain response (at f≊10 kHz) of a magnetostrictive oscillator. Low frequency (${\mathit{f}}_{\mathrm{mod}}$≤0.1 Hz) modulation of the observed subcritical bifurcation provides a phase-reversing time series whose power spectrum tends to conceal frequency components. An event counting technique developed for characterizing the phase-slip dynamics of the time series reveals a substantial component at half the modulation frequency (f/2) as well as at f. The event counting technique is applied to observe stochastic resonance for the first time in a tristable system.

The transition to spatiotemporal chaos in the neighborhood of a codimension-two point observed in the Taylor-Dean system is investigated. The initial instability is to stationary Dean vortex flow, which becomes unstable to a drift instability, followed by a wavelength-halving instability. This sequence of transitions may be explained in terms of the interaction between the first and second spatial harmonics of the basic pattern.

Using numerical methods we find that anti-Stokes generation in stimulated Raman scattering can cause Raman solitons to decay, unless the fields are phase matched. Photon number conservation then leads to unusually high intensities in regions where both the Stokes and anti-Stokes fields vanish. For large propagation lengths, the pump soliton can decay considerably, and as a result, the fields do not interact strongly. We therefore predict the formation of solitonlike pulses at the anti-Stokes frequency.