2,703 research outputs found
Wave propagation into the middle atmosphere
Recent observations of various types of waves propagating into the middle atmosphere are reviewed. Emphasis is made on the excitation processes in the lower atmosphere and their vertical propagation through the background flow as a function of the latitude, height and season. The following subjects are discussed: (1) Vertical propagation of quasi-stationary forced Rossby waves into the winter stratosphere in connection with the sudden warming; (2) Spectral distribution and seasonal characteristics of normal mode (free) Rossby waves and the asymmetry of the Northern and Southern Hemispheres; and (3) Seasonal variation of internal gravity waves in the middle atmosphere. Further discussions are presented for future studies based on accumulated observational data during the MAP period
A new integrable system related to the Toda lattice
A new integrable lattice system is introduced, and its integrable
discretizations are obtained. A B\"acklund transformation between this new
system and the Toda lattice, as well as between their discretizations, is
established.Comment: LaTeX, 14 p
Handbook for MAP, volume 32. Part 1: MAP summary. Part 2: MAPSC minutes, reading, August 1989. MAP summaries from nations. Part 3: MAP data catalogue
Extended abstracts from the fourth workshop on the technical and scientific aspects of mesosphere stratosphere troposphere (MST) radar are presented. Individual sessions addressed the following topics: meteorological applications of MST and ST radars, networks, and campaigns; the dynamics of the equatorial middle atmosphere; interpretation of radar returns from clear air; techniques for studying gravity waves and turbulence, intercomparison and calibration of wind and wave measurements at various frequencies; progress in existing and planned MST and ST radars; hardware design for MST and ST radars and boundary layer/lower troposphere profilers; signal processing; and data management
An integrable generalization of the Toda law to the square lattice
We generalize the Toda lattice (or Toda chain) equation to the square
lattice; i.e., we construct an integrable nonlinear equation, for a scalar
field taking values on the square lattice and depending on a continuous (time)
variable, characterized by an exponential law of interaction in both discrete
directions of the square lattice. We construct the Darboux-Backlund
transformations for such lattice, and the corresponding formulas describing
their superposition. We finally use these Darboux-Backlund transformations to
generate examples of explicit solutions of exponential and rational type. The
exponential solutions describe the evolution of one and two smooth
two-dimensional shock waves on the square lattice.Comment: 14 pages, 4 figures, to appear in Phys. Rev. E http://pre.aps.org
Pfaffian and Determinant Solutions to A Discretized Toda Equation for and
We consider a class of 2 dimensional Toda equations on discrete space-time.
It has arisen as functional relations in commuting family of transfer matrices
in solvable lattice models associated with any classical simple Lie algebra
. For and , we present the solution in terms of
Pfaffians and determinants. They may be viewed as Yangian analogues of the
classical Jacobi-Trudi formula on Schur functions.Comment: Plain Tex, 9 page
Solutions of a discretized Toda field equation for from Analytic Bethe Ansatz
Commuting transfer matrices of vertex models obey the
functional relations which can be viewed as an type Toda field equation
on discrete space time. Based on analytic Bethe ansatz we present, for
, a new expression of its solution in terms of determinants and
Pfaffians.Comment: Latex, 14 pages, ioplppt.sty and iopl12.sty assume
Integrable dynamics of Toda-type on the square and triangular lattices
In a recent paper we constructed an integrable generalization of the Toda law
on the square lattice. In this paper we construct other examples of integrable
dynamics of Toda-type on the square lattice, as well as on the triangular
lattice, as nonlinear symmetries of the discrete Laplace equations on the
square and triangular lattices. We also construct the - function
formulations and the Darboux-B\"acklund transformations of these novel
dynamics.Comment: 22 pages, 4 figure
Supersymmetric Modified Korteweg-de Vries Equation: Bilinear Approach
A proper bilinear form is proposed for the N=1 supersymmetric modified
Korteweg-de Vries equation. The bilinear B\"{a}cklund transformation of this
system is constructed. As applications, some solutions are presented for it.Comment: 8 pages, LaTeX using packages amsmath and amssymb, some corrections
mad
A survey of Hirota's difference equations
A review of selected topics in Hirota's bilinear difference equation (HBDE)
is given. This famous 3-dimensional difference equation is known to provide a
canonical integrable discretization for most important types of soliton
equations. Similarly to the continuous theory, HBDE is a member of an infinite
hierarchy. The central point of our exposition is a discrete version of the
zero curvature condition explicitly written in the form of discrete
Zakharov-Shabat equations for M-operators realized as difference or
pseudo-difference operators. A unified approach to various types of M-operators
and zero curvature representations is suggested. Different reductions of HBDE
to 2-dimensional equations are considered. Among them discrete counterparts of
the KdV, sine-Gordon, Toda chain, relativistic Toda chain and other typical
examples are discussed in detail.Comment: LaTeX, 43 pages, LaTeX figures (with emlines2.sty
Integrability of one degree of freedom symplectic maps with polar singularities
In this paper, we treat symplectic difference equations with one degree of
freedom. For such cases, we resolve the relation between that the dynamics on
the two dimensional phase space is reduced to on one dimensional level sets by
a conserved quantity and that the dynamics is integrable, under some
assumptions. The process which we introduce is related to interval exchange
transformations.Comment: 10 pages, 2 figure
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