16,361 research outputs found
Spectral theory of soliton and breather gases for the focusing nonlinear Schrödinger equation
Solitons and breathers are localized solutions of integrable systems that can be viewed as “particles” of complex statistical objects called soliton and breather gases. In view of the growing evidence of their ubiquity in fluids and nonlinear optical media, these “integrable” gases present a fundamental interest for nonlinear physics. We develop an analytical theory of breather and soliton gases by considering a special, thermodynamic-type limit of the wave-number–frequency relations for multiphase (finite-gap) solutions of the focusing nonlinear Schrödinger equation. This limit is defined by the locus and the critical scaling of the band spectrum of the associated Zakharov-Shabat operator, and it yields the nonlinear dispersion relations for a spatially homogeneous breather or soliton gas, depending on the presence or absence of the “background” Stokes mode. The key quantity of interest is the density of states defining, in principle, all spectral and statistical properties of a soliton (breather) gas. The balance of terms in the nonlinear dispersion relations determines the nature of the gas: from an ideal gas of well separated, noninteracting breathers (solitons) to a special limiting state, which we term a breather (soliton) condensate, and whose properties are entirely determined by the pairwise interactions between breathers (solitons). For a nonhomogeneous breather gas, we derive a full set of kinetic equations describing the slow evolution of the density of states and of its carrier wave counterpart. The kinetic equation for soliton gas is recovered by collapsing the Stokes spectral band. A number of concrete examples of breather and soliton gases are considered, demonstrating the efficacy of the developed general theory with broad implications for nonlinear optics, superfluids, and oceanography. In particular, our work provides the theoretical underpinning for the recently observed remarkable connection of the soliton gas dynamics with the long-term evolution of spontaneous modulational instability
Measurements of the Influence of Acceleration and Temperature of Bodies on their Weight
A brief review of experimental research of the influence of acceleration and
temperatures of test mass upon gravitation force, executed between the 1990s
and the beginning of 2000 is provided.Results of weighing a rotor of a
mechanical gyroscope with a horizontal axis, an anisotropic crystal with the
big difference of the speed of longitudinal acoustic waves, measurements of
temperature dependence of weight of metal bars of non-magnetic materials, and
also measurement of restitution coefficients at quasi-elastic impact of a steel
ball about a massive plate are given. A negative temperature dependence of the
weight of a brass core was measured. All observably experimental effects, have
probably a general physical reason connected with the weight change dependent
upon acceleration of a body or at thermal movement of its microparticles.Comment: 7 pages, 6 figures. Presented at the 5-th Symposium on New Frontiers
and Future Concepts (STAIF-2008
Cyclicity in weighted Bergman type spaces
We use the so called resolvent transform method to study the cyclicity of the
one point mass singular inner function in weighted Bergman type spaces.Comment: 20 page
Unified Approach to KdV Modulations
We develop a unified approach to integrating the Whitham modulation
equations. Our approach is based on the formulation of the initial value
problem for the zero dispersion KdV as the steepest descent for the scalar
Riemann-Hilbert problem, developed by Deift, Venakides, and Zhou, 1997, and on
the method of generating differentials for the KdV-Whitham hierarchy proposed
by El, 1996. By assuming the hyperbolicity of the zero-dispersion limit for the
KdV with general initial data, we bypass the inverse scattering transform and
produce the symmetric system of algebraic equations describing motion of the
modulation parameters plus the system of inequalities determining the number
the oscillating phases at any fixed point on the - plane. The resulting
system effectively solves the zero dispersion KdV with an arbitrary initial
data.Comment: 27 pages, Latex, 5 Postscript figures, to be submitted to Comm. Pure.
Appl. Mat
Dam break problem for the focusing nonlinear Schr\"odinger equation and the generation of rogue waves
We propose a novel, analytically tractable, scenario of the rogue wave
formation in the framework of the small-dispersion focusing nonlinear
Schr\"odinger (NLS) equation with the initial condition in the form of a
rectangular barrier (a "box"). We use the Whitham modulation theory combined
with the nonlinear steepest descent for the semi-classical inverse scattering
transform, to describe the evolution and interaction of two counter-propagating
nonlinear wave trains --- the dispersive dam break flows --- generated in the
NLS box problem. We show that the interaction dynamics results in the emergence
of modulated large-amplitude quasi-periodic breather lattices whose amplitude
profiles are closely approximated by the Akhmediev and Peregrine breathers
within certain space-time domain. Our semi-classical analytical results are
shown to be in excellent agreement with the results of direct numerical
simulations of the small-dispersion focusing NLS equation.Comment: 29 pages, 15 figures, major revisio
The pseudo-self-similar traffic model: application and validation
Since the early 1990¿s, a variety of studies has shown that network traffic, both for local- and wide-area networks, has self-similar properties. This led to new approaches in network traffic modelling because most traditional traffic approaches result in the underestimation of performance measures of interest. Instead of developing completely new traffic models, a number of researchers have proposed to adapt traditional traffic modelling approaches to incorporate aspects of self-similarity. The motivation for doing so is the hope to be able to reuse techniques and tools that have been developed in the past and with which experience has been gained. One such approach for a traffic model that incorporates aspects of self-similarity is the so-called pseudo self-similar traffic model. This model is appealing, as it is easy to understand and easily embedded in Markovian performance evaluation studies. In applying this model in a number of cases, we have perceived various problems which we initially thought were particular to these specific cases. However, we recently have been able to show that these problems are fundamental to the pseudo self-similar traffic model. In this paper we review the pseudo self-similar traffic model and discuss its fundamental shortcomings. As far as we know, this is the first paper that discusses these shortcomings formally. We also report on ongoing work to overcome some of these problems
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