1,615 research outputs found
On the classification of conditionally integrable evolution systems in (1+1) dimensions
We generalize earlier results of Fokas and Liu and find all locally analytic
(1+1)-dimensional evolution equations of order that admit an -shock type
solution with .
To this end we develop a refinement of the technique from our earlier work
(A. Sergyeyev, J. Phys. A: Math. Gen, 35 (2002), 7653--7660), where we
completely characterized all (1+1)-dimensional evolution systems
\bi{u}_t=\bi{F}(x,t,\bi{u},\p\bi{u}/\p x,...,\p^n\bi{u}/\p x^n) that are
conditionally invariant under a given generalized (Lie--B\"acklund) vector
field \bi{Q}(x,t,\bi{u},\p\bi{u}/\p x,...,\p^k\bi{u}/\p x^k)\p/\p\bi{u} under
the assumption that the system of ODEs \bi{Q}=0 is totally nondegenerate.
Every such conditionally invariant evolution system admits a reduction to a
system of ODEs in , thus being a nonlinear counterpart to quasi-exactly
solvable models in quantum mechanics.
Keywords: Exact solutions, nonlinear evolution equations, conditional
integrability, generalized symmetries, reduction, generalized conditional
symmetries
MSC 2000: 35A30, 35G25, 81U15, 35N10, 37K35, 58J70, 58J72, 34A34Comment: 8 pages, LaTeX 2e, now uses hyperre
Rigorous 3D inversion of marine CSEM data based on the integral equation method
Journal ArticleMarine controlled-source electromagnetic (MCSEM) surveys have become an important part of offshore petroleum exploration. However, due to enormous computational difficulties with full 3D inversion, practical interpretation of MCSEM data is still a very challenging problem. We present a new approach to 3D inversion of MCSEM data based on rigorous integral-equation (IE) forward modeling and a new IE representation of the sensitivity (Fréchet derivative matrix) of observed data to variations in sea-bottom conductivity. We develop a new form of the quasi-analytical approximation for models with variable background conductivity (QAVB) and apply this form for more efficient Fréchet derivative calculations. This approach requires just one forward modeling on every iteration of the regularized gradient-type inversion algorithm, which speeds up the computations significantly. We also use a regularized focusing inversion method, which provides a sharp boundary image of the petroleum reservoir. The methodology is tested on a 3D inversion of the synthetic EM data representing a typical MCSEM survey conducted for offshore petroleum exploration
Formation of singularities on the surface of a liquid metal in a strong electric field
The nonlinear dynamics of the free surface of an ideal conducting liquid in a
strong external electric field is studied. It is establish that the equations
of motion for such a liquid can be solved in the approximation in which the
surface deviates from a plane by small angles. This makes it possible to show
that on an initially smooth surface for almost any initial conditions points
with an infinite curvature corresponding to branch points of the root type can
form in a finite time.Comment: 14 page
Direct observation of mode-coupling instability in two-dimensional plasma crystals
Dedicated experiments on melting of 2D plasma crystals were carried out. The
melting was always accompanied by spontaneous growth of the particle kinetic
energy, suggesting a universal plasma-driven mechanism underlying the process.
By measuring three principal dust-lattice (DL) wave modes simultaneously, it is
unambiguously demonstrated that the melting occurs due to the resonance
coupling between two of the DL modes. The variation of the wave modes with the
experimental conditions, including the emergence of the resonant (hybrid)
branch, reveals exceptionally good agreement with the theory of mode-coupling
instability.Comment: 4 pages, submitted to Physical Review Letter
First direct measurement of optical phonons in 2D plasma crystals
Spectra of phonons with out-of-plane polarization were studied experimentally
in a 2D plasma crystal. The dispersion relation was directly measured for the
first time using a novel method of particle imaging. The out-of-plane mode was
proven to have negative optical dispersion, comparison with theory showed good
agreement. The effect of the plasma wakes on the dispersion relation is briefly
discussed.Comment: submitted to Physical Review Letter
Wave mode coupling due to plasma wakes in two-dimensional plasma crystals: In-depth view
Experiments with two-dimensional (2D) plasma crystals are usually carried out
in rf plasma sheaths, where the interparticle interactions are modified due to
the presence of plasma wakes. The wake-mediated interactions result in the
coupling between wave modes in 2D crystals, which can trigger the mode-coupling
instability and cause melting. The theory predicts a number of distinct
fingerprints to be observed upon the instability onset, such as the emergence
of a new hybrid mode, a critical angular dependence, a mixed polarization, and
distinct thresholds. In this paper we summarize these key features and provide
their detailed discussion, analyze the critical dependence on experimental
parameters, and highlight the outstanding issues
Group classification of heat conductivity equations with a nonlinear source
We suggest a systematic procedure for classifying partial differential
equations invariant with respect to low dimensional Lie algebras. This
procedure is a proper synthesis of the infinitesimal Lie's method, technique of
equivalence transformations and theory of classification of abstract low
dimensional Lie algebras. As an application, we consider the problem of
classifying heat conductivity equations in one variable with nonlinear
convection and source terms. We have derived a complete classification of
nonlinear equations of this type admitting nontrivial symmetry. It is shown
that there are three, seven, twenty eight and twelve inequivalent classes of
partial differential equations of the considered type that are invariant under
the one-, two-, three- and four-dimensional Lie algebras, correspondingly.
Furthermore, we prove that any partial differential equation belonging to the
class under study and admitting symmetry group of the dimension higher than
four is locally equivalent to a linear equation. This classification is
compared to existing group classifications of nonlinear heat conductivity
equations and one of the conclusions is that all of them can be obtained within
the framework of our approach. Furthermore, a number of new invariant equations
are constructed which have rich symmetry properties and, therefore, may be used
for mathematical modeling of, say, nonlinear heat transfer processes.Comment: LaTeX, 51 page
Mobile application for archaeological exploration
Is described the problem of automation of the archaeological exploration. Is developed mobile GIS application for its decision.Рассматривается задача автоматизации археологической разведки. Разрабатывается мобильное геоинформационное приложение для ее решения
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