2,452 research outputs found
On integration of some classes of dimensional nonlinear Partial Differential Equations
The paper represents the method for construction of the families of
particular solutions to some new classes of dimensional nonlinear
Partial Differential Equations (PDE). Method is based on the specific link
between algebraic matrix equations and PDE. Admittable solutions depend on
arbitrary functions of variables.Comment: 6 page
Variational approach for the quantum Zakharov system
The quantum Zakharov system is described in terms of a Lagrangian formalism.
A time-dependent Gaussian trial function approach for the envelope electric
field and the low-frequency part of the density fluctuation leads to a coupled,
nonlinear system of ordinary differential equations. In the semiclassic case,
linear stability analysis of this dynamical system shows a destabilizing r\^ole
played by quantum effects. Arbitrary value of the quantum effects are also
considered, yielding the ultimate destruction of the localized, Gaussian trial
solution. Numerical simulations are shown both for the semiclassic and the full
quantum cases.Comment: 6 figure
Partially integrable systems in multidimensions by a variant of the dressing method. 1
In this paper we construct nonlinear partial differential equations in more
than 3 independent variables, possessing a manifold of analytic solutions with
high, but not full, dimensionality. For this reason we call them ``partially
integrable''. Such a construction is achieved using a suitable modification of
the classical dressing scheme, consisting in assuming that the kernel of the
basic integral operator of the dressing formalism be nontrivial. This new
hypothesis leads to the construction of: 1) a linear system of compatible
spectral problems for the solution of the integral equation in 3
independent variables each (while the usual dressing method generates spectral
problems in 1 or 2 dimensions); 2) a system of nonlinear partial differential
equations in dimensions (), possessing a manifold of analytic
solutions of dimension (), which includes one largely arbitrary relation
among the fields. These nonlinear equations can also contain an arbitrary
forcing.Comment: 21 page
Polynomial spline-approximation of Clarke's model
We investigate polynomial spline approximation of stationary random processes on a uniform grid applied to Clarke's model of time variations of path amplitudes in multipath fading channels with Doppler scattering. The integral mean square error (MSE) for optimal and interpolation splines is presented as a series of spectral moments. The optimal splines outperform the interpolation splines; however, as the sampling factor increases, the optimal and interpolation splines of even order tend to provide the same accuracy. To build such splines, the process to be approximated needs to be known for all time, which is impractical. Local splines, on the other hand, may be used where the process is known only over a finite interval. We first consider local splines with quasioptimal spline coefficients. Then, we derive optimal spline coefficients and investigate the error for different sets of samples used for calculating the spline coefficients. In practice, approximation with a low processing delay is of interest; we investigate local spline extrapolation with a zero-processing delay. The results of our investigation show that local spline approximation is attractive for implementation from viewpoints of both low processing delay and small approximation error; the error can be very close to the minimum error provided by optimal splines. Thus, local splines can be effectively used for channel estimation in multipath fast fading channels
Long-distance radiative corrections to the di-pion tau lepton decay
We evaluate the model-dependent piece of O(alpha) long-distance radiative
corrections to tau^- \to \pi^- \pi^0\nu_{\tau} decays by using a meson
dominance model. We find that these corrections to the di-pion invariant mass
spectrum are smaller than in previous calculations based on chiral perturbation
theory. The corresponding correction to the photon inclusive rate is tiny
(-0.15%) but it can be of relevance when new measurements reach better
precision.Comment: 4 pages, 2 figures. An estimate of the shift produced in the
evaluation of the h.v.p. contribution to the muon anomalous magnetic moment
is added. Version to appear in Phys. Rev.
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