4,238 research outputs found
Non-Hamiltonian generalizations of the dispersionless 2DTL hierarchy
We consider two-component integrable generalizations of the dispersionless
2DTL hierarchy connected with non-Hamiltonian vector fields, similar to the
Manakov-Santini hierarchy generalizing the dKP hierarchy. They form a
one-parametric family connected by hodograph type transformations. Generating
equations and Lax-Sato equations are introduced, a dressing scheme based on the
vector nonlinear Riemann problem is formulated. The simplest two-component
generalization of the dispersionless 2DTL equation is derived, its differential
reduction analogous to the Dunajski interpolating system is presented. A
symmetric two-component generalization of the dispersionless elliptic 2DTL
equation is also constructed.Comment: 10 pages, the text of the talk at NEEDS 09. Notations clarified,
references adde
`Interpolating' differential reductions of multidimensional integrable hierarchies
We transfer the scheme of constructing differential reductions, developed
recently for the case of the Manakov-Santini hierarchy, to the general
multidimensional case. We consider in more detail the four-dimensional case,
connected with the second heavenly equation and its generalization proposed by
Dunajski. We give a characterization of differential reductions in terms of the
Lax-Sato equations as well as in the framework of the dressing method based on
nonlinear Riemann-Hilbert problem.Comment: Based on the talk at NLPVI, Gallipoli, 15 page
On the heavenly equation hierarchy and its reductions
Second heavenly equation hierarchy is considered using the framework of
hyper-K\"ahler hierarchy developed by Takasaki. Generating equations for the
hierarchy are introduced, they are used to construct generating equations for
reduced hierarchies. General -reductions, logarithmic reduction and rational
reduction for one of the Lax-Sato functions are discussed. It is demonstrated
that rational reduction is equivalent to the symmetry constraint.Comment: 13 pages, LaTeX, minor misprints corrected, references adde
On a class of reductions of Manakov-Santini hierarchy connected with the interpolating system
Using Lax-Sato formulation of Manakov-Santini hierarchy, we introduce a class
of reductions, such that zero order reduction of this class corresponds to dKP
hierarchy, and the first order reduction gives the hierarchy associated with
the interpolating system introduced by Dunajski. We present Lax-Sato form of
reduced hierarchy for the interpolating system and also for the reduction of
arbitrary order. Similar to dKP hierarchy, Lax-Sato equations for (Lax
fuction) due to the reduction split from Lax-Sato equations for (Orlov
function), and the reduced hierarchy for arbitrary order of reduction is
defined by Lax-Sato equations for only. Characterization of the class of
reductions in terms of the dressing data is given. We also consider a waterbag
reduction of the interpolating system hierarchy, which defines
(1+1)-dimensional systems of hydrodynamic type.Comment: 15 pages, revised and extended, characterization of the class of
reductions in terms of the dressing data is give
Grassmannians Gr(N-1,N+1), closed differential N-1 forms and N-dimensional integrable systems
Integrable flows on the Grassmannians Gr(N-1,N+1) are defined by the
requirement of closedness of the differential N-1 forms of rank
N-1 naturally associated with Gr(N-1,N+1). Gauge-invariant parts of these
flows, given by the systems of the N-1 quasi-linear differential equations,
describe coisotropic deformations of (N-1)-dimensional linear subspaces. For
the class of solutions which are Laurent polynomials in one variable these
systems coincide with N-dimensional integrable systems such as Liouville
equation (N=2), dispersionless Kadomtsev-Petviashvili equation (N=3),
dispersionless Toda equation (N=3), Plebanski second heavenly equation (N=4)
and others. Gauge invariant part of the forms provides us with
the compact form of the corresponding hierarchies. Dual quasi-linear systems
associated with the projectively dual Grassmannians Gr(2,N+1) are defined via
the requirement of the closedness of the dual forms . It
is shown that at N=3 the self-dual quasi-linear system, which is associated
with the harmonic (closed and co-closed) form , coincides with the
Maxwell equations for orthogonal electric and magnetic fields.Comment: 26 pages, references adde
Dunajski generalization of the second heavenly equation: dressing method and the hierarchy
Dunajski generalization of the second heavenly equation is studied. A
dressing scheme applicable to Dunajski equation is developed, an example of
constructing solutions in terms of implicit functions is considered. Dunajski
equation hierarchy is described, its Lax-Sato form is presented. Dunajsky
equation hierarchy is characterized by conservation of three-dimensional volume
form, in which a spectral variable is taken into account.Comment: 13 page
Spin-flop transition in uniaxial antiferromagnets: magnetic phases, reorientation effects, multidomain states
The classical spin-flop is the field-driven first-order reorientation
transition in easy-axis antiferromagnets. A comprehensive phenomenological
theory of easy-axis antiferromagnets displaying spin-flops is developed. It is
shown how the hierarchy of magnetic coupling strengths in these
antiferromagnets causes a strongly pronounced two-scale character in their
magnetic phase structure. In contrast to the major part of the magnetic phase
diagram, these antiferromagnets near the spin-flop region are described by an
effective model akin to uniaxial ferromagnets. For a consistent theoretical
description both higher-order anisotropy contributions and dipolar stray-fields
have to be taken into account near the spin-flop. In particular,
thermodynamically stable multidomain states exist in the spin-flop region,
owing to the phase coexistence at this first-order transition. For this region,
equilibrium spin-configurations and parameters of the multidomain states are
derived as functions of the external magnetic field. The components of the
magnetic susceptibility tensor are calculated for homogeneous and multidomain
states in the vicinity of the spin-flop. The remarkable anomalies in these
measurable quantities provide an efficient method to investigate magnetic
states and to determine materials parameters in bulk and confined
antiferromagnets, as well as in nanoscale synthetic antiferromagnets. The
method is demonstrated for experimental data on the magnetic properties near
the spin-flop region in the orthorhombic layered antiferromagnet
(C_2H_5NH_3)_2CuCl_4.Comment: (15 pages, 12 figures; 2nd version: improved notation and figures,
correction of various typos
Evaluation of the current state of aquatic ecosystems and the problems of the protection of biological resources during development of kruzenshternskoye gcf
The results of studies of the current state of freshwater ecosystems and their biotic components in the western part of the Yamal Peninsula are presented in the article. Based on the evaluation of the structure of communities of phytoplankton, zooplankton, benthos, and whitefishes, the range of problems related to the protection of biological resources during the development of the Kruzenshternskoye gas field is defined. The data on species composition and quantitative indicators of hydrobionts of different types of waterbodies and watercourses in the lower reaches of the Mordyyakha and Naduyyakha Rivers basins is the basis for environmental monitoring of water objects during development and exploitation of the Kruzenshternskoye gas field. Estimation of the fish fauna state and their food base in the territory of the Kruzenshternskoye GCF according to the monitoring program is present. The river delta zones are the most important feeding areas of the salmonid and whitefishes valuable fish species in the territory of Kruzenshternskoye GCF. In cases where water bodies and watercourses are not completely demolished for the construction of GCF facilities, changes of quantitative and qualitative characteristics of communities of hydrobionts after the end of operations are reversible. River ecosystems are restored within a shorter period of time in comparison to lacustrine ones. Proposals for the protection of fisheries resources and monitoring of aquatic ecosystems on the basis of comprehensive studies are reported. Recommendations on reducing the anthropogenic impact on aquatic ecosystems in the development period are present. The results of the investigation were used in the development of the environmental protection part of the Kruzenshternskoye deposit project. Anthropogenic disturbances present now on the gas deposit territory of Kruzenshternskoye does not influence the aquatic ecosystems.The article have been prepared within the Project of the Presidium of the Russian Academy of Sciences № 12-P-47-2013 and "The Arctic" Project of the Presidium of the Ural Branch of the Russian Academy of Sciences № 12-4-3-012
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