We performed a systematic analysis of exact solutions for the higher-order nonlinear Schrödinger equation i${\mathrm{\psi }}_{\mathit{X}}$+${\mathrm{\psi }}_{\mathit{T}\mathit{T}}$=${\mathit{a}}_1$ψ‖ψ${\mathrm{\Vert }}^2$+${\mathit{a}}_2$ψ‖ψ${\mathrm{\Vert }}^4$+${\mathit{ia}}_3$ (ψ‖ψ${\mathrm{\Vert }}^2$${)}_{\mathit{T}}$+(${\mathit{a}}_4$+${\mathit{ia}}_5$)ψ(‖ψ${\mathrm{\Vert }}^2$${)}_{\mathit{T}}$ that describes wave propagation in nonlinear dispersive media. The method consists of the determination of all transformations that reduce the equation to ordinary differential equations that are solved whenever possible. All obtained solutions fall into one of the following categories: ‘‘bright’’ or ‘‘dark’’ solitary waves, solitonic waves, regular and singular periodic waves, shock waves, accelerating waves, and self-similar solutions. They are expressed in terms of simple functions except for few cases given in terms of the less-known Painlevé transcendents.

An effective-medium theory for nonlinear spherical particles embedded in a linear host medium is developed. The formulation is based on a T-matrix approach. Introduction of a field-dependent T matrix enables one to obtain an exact expression for effective dielectric constant of a medium with spherical grains. In the special cases of low-field values, the results obtained previously for the third- and fifth-order nonlinear susceptibilities of the medium are recovered. The resonance behavior of the effective dielectric constant and intrinsic optical bistability are also discussed.

The free energy of a one-dimensional anharmonic oscillator is evaluated using the path-integral formalism. A result is derived for small to moderate values of g${\mathrm{\beta }}^3$, where g measures the anharmonicity and β is the inverse temperature. In the case of small g${\mathrm{\beta }}^3$ our result interpolates the classical limit (βω≪1) and the perturbation limit (g/β${\mathrm{\omega }}^4$≪1).

A form of the Gibbs-Bogoliubov statistical-mechanical variational principle is enunciated that is well adapted to systems in which the electrons are treated quantum mechanically but the nuclei may be treated classically. An initial variational solution for fixed nuclear positions yields a statistical Born-Oppenheimer potential that serves as input for a variational evaluation of the nuclear configurational free energy.

The Ulam model analog of the Fermi acceleration for the sine-Gordon solitons is investigated. The motion of soliton between two potential walls, one of which is periodically oscillating, is studied. With the help of the Melnikov method the expression for the threshold of stochasticity in soliton motion is found.

In a recent paper by one of us (D. J. E.) and Lynden-Bell [Phys. Rev. A 38, 5249 (1988)], simple equilibrium expressions were obtained for the nonlinear Burnett coefficients for a model of electrical conductivity. In this paper we show how these expressions can be generalized to an arbitrary transport coefficient.

The kinetic equation of a quantum plasma is given in the spatially quasihomogeneous case. The equation includes the quantum effect and the many-body effect. The kinetic shielding potential produced by the many-body effect is discussed.

We develop an effective interface formalism design to provide an analytical understanding of the global stability properties of array structures in interfacial pattern-forming systems. This formalism is applied to perform the linear stability analysis of long-wavelength perturbations of a periodic array of Saffman-Taylor fingers. The breaking of the translational symmetry in the direction of propagation leads to an unstable mode analogous to the one which develops from the planar interface. The breaking of the translational symmetry in the transverse direction leads to a mode that, unlike the Eckhaus mode characteristic of small amplitude periodic structures, is always stable.

We show theoretically and experimentally that a homeotropically aligned nematic cell can exhibit bistability in response to rotation of an applied magnetic field. Two stable configurations of molecular reorientation exist when the applied field is stronger than the Fréedericksz threshold value and its tilt angle away from the homeotropic alignment falls into a specific range. Switching in bistable operation was observed and found to be in good agreement with theory.

A micellar solution model is considered to exemplify an atypical source of corrections to scaling occurring for systems equivalent to simple Ising models but with temperature-dependent interactions. The mixture and its Ising image differ in reduced temperature scales, and these relate through a nonanalytical transformation when other critical points fall within the temperature range of interest. Universality is always preserved; however, effective exponents may persist unusually close to criticality.

A family of the exact and analytical solutions of the equilibrium shape equation of vesicle membranes is found. They are anchor rings with generating circles of radii in the ratio 1/ √2 . It is shown that these ring vesicles are stable for some negative values of their spontaneous curvatures, such that experimental construction of such vesicles seems possible. A discussion shows that a positive Gauss-curvature elastic modulus favors the formation of these special vesicles.

An effective pair potential for liquid sodium near freezing has been calculated from electron theory using the density-functional method. The main features of the potential extracted by Reatto, Levesque, and Weis [Phys. Rev. A 33, 3451 (1986)] by inverting the measured structure factor of Greenfield, Wellendorf, and Wiser [Phys. Rev. A 4, 1607 (1971)] are faithfully reflected by electron theory. To obtain precise agreement between the two methods will evidently require further progress in setting up nonlocal exchange and correlation functionals.

The effect of using different algorithms to simulate reaction-limited cluster-cluster aggregation is studied. Small differences in the scaling behavior are found, which when examined suggest the existence of an alternative, slow approach to scaling common to all the algorithms tested. The probable explanation in terms of the weighting assigned to multiple-contact configurations is explored.

Results are presented of experimental research aimed at the study of hydrodynamic processes and soft-x-ray (SXR) emission characteristics of a laser-produced plasma in a half-cylindrical-shell target. Experimental measurements show that this kind of target can effectively increase the short-wavelength SXR emission of the laser-produced plasma in the grooved region.

A possible contribution of negative atomic ions to the continuum radiation in nitrogen plasma is discussed. It is shown that both unstable ${\mathrm{N}}^{\mathrm{-}}$${(}^3$P) and metastable ${\mathrm{N}}^{\mathrm{-}}$${(}^1$D) ions may have a significant effect on the total production of the continuum radiation at electron temperatures below 12000 K. It is also suggested that the theoretical cross sections for the radiative attachments involving the negative ions are more reliable than the available experimental cross sections.

An electric transmission line periodically 100-LC-circuit loaded with variable-capacitance diodes has been constructed to study solitary-wave (soliton) formation in a dispersive medium. A rectangular pulse fed into the nonlinear, lumped LC transmission line has been observed to be steepened by the nonlinear effect at the early stages. The steepened signal has been observed to decrease and broaden during propagation along the line and eventually change into solitons at around the seventh or eighth stage by a delicate balance between the nonlinear effect due to voltage-dependent capacitance and the dispersion effect due to the LC circuit.

The paper deals with the nonlinear Schrödinger equation perturbed by a nonlinear dissipative term, which, however, conserves the plasmon number (wave action). Such terms describe the nonlinear Landau damping in plasmas or the Raman-scattering-induced dissipation in a nonlinear optical medium. The perturbing term drives a soliton as a constant force, leaving its amplitude unchanged. It is demonstrated that collisions between the driven solitons give rise to radiative losses of the plasmon number. Next, the kinetics of a rarefied soliton gas is analyzed, and it is shown that collisions result in complete decay of solitons into radiation. An asymptotic law of the decay is found.

A filter-lens combination in conjunction with partially coherent light is used to produce a secondary source that violates a certain scaling law. The spectral shifts observed have been found to be dependent on the complex degree of spectral coherence, filter peak transmission wavelength, and half-band-width of the filter.

We show that the continuum and semidiscrete approximations break down for the propagation of pulses in a nonlinear model developed to mimic some dynamic aspects of the DNA double helix. The model assumes nonlinear behavior for the interbase hydrogen bonds. The effects of longer-range interactions and additional nonlinearities of the system are explored. Numerical solutions showing the effects of these additional factors are displayed.

A recent Brief Report [N. H. March and B. V. Paranjape, Phys. Rev. A 35, 5285 (1987)] is based on an incorrect formula for the dynamical structure factor S(k,ω). This leads to an incorrect sound velocity.