37,263 research outputs found
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
A windowless apparatus was constructed and used to measure the photoabsorption and fluorescence cross sections of molecules in the extreme ultraviolet region. Photoabsorption and fluorescence cross sections of H2O, D2O, H2S, D2s, and Co were measured in the 50 to 200 nm region. These quantitative data are currently needed for the determination of the formulation and destruction rates of molecules in the interstellar medium
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