Soliton-like solutions for the nonlinear schr?dinger equation with variable quadratic hamiltonians

We construct one-soliton solutions for the nonlinear Schr¨odinger equation with variable quadratic Hamiltonians in a unified form by taking advantage of the complete (super) integrability of generalized harmonic oscillators. The soliton-wave evolution in external fields with variable quadratic potentials is totally determined by the linear problem, like motion of a classical particle with acceleration, and the (self-similar) soliton shape is due to a subtle balance between the linear Hamiltonian (dispersion and potential) and nonlinearity in the Schr¨odinger equation by the standards of soliton theory. Most linear (hypergeometric, Bessel) and a few nonlinear (Jacobian elliptic, second Painlev′e transcendental) classical special functions of mathematical physics are linked together through these solutions, thus providing a variety of nonlinear integrable cases. Examples include bright and dark solitons and Jacobi elliptic and second Painlev′e transcendental solutions for several variable Hamiltonians that are important for research in nonlinear optics, plasma physics, and Bose–Einstein condensation. The Feshbach-resonance matter-wave-soliton management is briefly discussed from this new perspective.     

Renormalization group functions of the φ<Superscript>4</Superscript> theory in the strong coupling limit: Analytical results

The previous attempts of reconstructing the Gell-Mann-Low function β(g) of the φ⁴ theory by summing perturbation series give the asymptotic behavior β(g) = β_∞ g in the limit g→∞, where α = 1 for the space dimensions d = 2, 3, 4. It can be hypothesized that the asymptotic behavior is β(g) ～ g for all d values. The consideration of the zero-dimensional case supports this hypothesis and reveals the mechanism of its appearance: it is associated with vanishing of one of the functional integrals. The generalization of the analysis confirms the asymptotic behavior β(g) ～ g in the general d-dimensional case. The asymptotic behaviors of other renormalization group functions are constant. The connection with the zero-charge problem and triviality of the φ⁴ theory is discussed.     

Compression and heating of spherical fusion targets by indirect (x-ray) drive on the Iskra-5 facility

Experiments have been carried out using the Iskra-5 facility in order to study the behavior of x-ray targets in response to a highly symmetric x-ray field. Results are presented of experiments using targets in the form of a spherical copper hohlraum coated with gold on the inside, with six laser entrance holes and a glass microtarget filled with DT gas located at the center. In some experiments the central capsule was coated with a plastic ablator layer of varying thickness. An analysis of the experimental results showed that on the whole, they are satisfactorily described by spherically symmetric gasdynamic calculations. Zh. éksp. Teor. Fiz. 114, 155–170 (July 1998)     

Classical orthogonal polynomials of a discrete variable on nonuniform lattices

A general theory of classical orthogonal polynomials of a discrete variable on nonuniform lattices is developed. The classification of the polynomials under consideration is given.     

Reactions of Some Terpenoids with CH-Acids in the Presence of Cs-β Zeolite

Reactions of some ,-unsaturated ketones from terpenoid series with CH-acids in the presence of Cs- zeolite were studied under various conditions. The variation of reaction conditions (heating, ultrasonic irradiation) strongly affected the reaction products ratio, and the effect was singular in each case and gave different results.     

Gell-Mann-Low function in QED

The Gell-Mann-Low function β(g) in QED (g is the fine structure constant) is reconstructed. At large g, it behaves as β_∞ g ^α with α≈1 and β_∞≈1.     

Estimate of the critical exponents from the field-theoretical renormalization group: mathematical meaning of the “Standard Values”

New estimates of the critical exponents have been obtained from the field-theoretical renormalization group using a new method for summing divergent series. The results almost coincide with the central values obtained by Le Guillou and Zinn-Justin (the so-called standard values), but have lower uncertainty. It has been shown that usual field-theoretical estimates implicitly imply the smoothness of the coefficient functions. The last assumption is open for discussion in view of the existence of the oscillating contribution to the coefficient functions. The appropriate interpretation of the last contribution is necessary both for the estimation of the systematic errors of the standard values and for a further increase in accuracy.     

Cross sections and asymmetries for elastic π3He scattering in the energy region around the Δ resonance

For a polarized target, π³He interaction is studied in the fixed-center approximation with all rescatterings included. Only the P ₃₃ wave is taken for the πN interaction. The nuclear wave function is taken either as a sum of Gaussian functions or as a Faddeev wave function in the s-wave approximation. The differential cross sections and asymmetries for elastic π⁺³He scattering at the laboratory energies of T _π, 180, and 256 MeV are calculated. The results are compared with experimental data.