A second look at the Gaussian semiclassical soliton ensemble for the focusing nonlinear Schr\"odinger equation

We present the results of a numerical experiment inspired by the semiclassical (zero-dispersion) limit of the focusing nonlinear Schroedinger (NLS) equation. In particular, we focus on the Gaussian semiclassical soliton ensemble, a family of exact multisoliton solutions obtained by repeatedly solving the initial-value problem for a particular sequence of initial data. The sequence of data is generated by adding an asymptotically vanishing sequence of perturbations to pure Gaussian initial data. These perturbations are obtained by applying the inverse-scattering transform to formal WKB approximations of eigenvalues of the associated spectral problem with a Gaussian potential. Recent results [Lee, Lyng, & Vankova, Physica D 24 (2012):1767--1781] suggest that, remarkably, these perturbations---interlaced as they are with the integrable structure of the equation---do not excite the acute modulational instabilities that are known to be present in the semiclassical regime. Here, we provide additional evidence to support the claim that these WKB-induced perturbations indeed have a very special structure. In particular, as a control experiment, we examine the evolution from a family of initial data created by an asymptotically vanishing family of analytic perturbations which are qualitatively indistinguishable from the WKB-induced perturbations that generate the Gaussian semiclassical soliton ensemble. We then compare this evolution to the (numerically computed) true evolution of the Gaussian and also to the evolution of the corresponding members of the semiclassical soliton ensemble. Our results both highlight the exceptional nature of the WKB-induced perturbations used to generate the semiclassical soliton ensemble and provide new insight into the sensitivity properties of the semiclassical limit problem for the focusing NLS equation

A Non-Principal Value Prescription for the Temporal Gauge

A non-principal value prescription is used to define the spurious singularities of Yang-Mills theory in the temporal gauge. Typical one-loop dimensionally-regularized temporal-gauge integrals in the prescription are explicitly calculated, and a regularization for the spurious gauge divergences is introduced. The divergent part of the one-loop self-energy is shown to be local and has the same form as that in the spatial axial gauge with the principal-value prescription. The renormalization of the theory is also briefly mentioned.Comment: 13 pages, NCKU-HEP/93-0

Measurement of HO2 chemical kinetics with a new detection method

Reaction rate constants of HO2+O3 were measured at various temperatures using a newly developed HO2 detection method. HO2 was detected by the OH(A-X) emission produced from photodissociative excitation of HO2 at 147 nm. In order to examine the possible interference of other emitting species with the HO2 detection, the photoexcitation processes of all the chemical species existing in the discharge flow tube were also investigated. The results are summarized

Photoabsorption and photodissociation of molecules important in the interstellar medium

The photo absorption, photo dissociation, and fluorescence cross sections of interstellar molecules and radicals were measured in the vacuum ultraviolet region. These quantitative optical data are useful for understanding of the formation and destruction processes of molecules under the intense interstellar W radiation field. Infrared (IR) emissions from W excitation of aromatic molecules were also observed in this research program. The research results are useful for studying the sources of the 'unidentified' interstellar infrared (UIR) emission bands