3,783 research outputs found
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
Continuous vacua in bilinear soliton equations
We discuss the freedom in the background field (vacuum) on top of which the
solitons are built. If the Hirota bilinear form of a soliton equation is given
by A(D_{\vec x})\bd GF=0,\, B(D_{\vec x})(\bd FF - \bd GG)=0 where both
and are even polynomials in their variables, then there can be a continuum
of vacua, parametrized by a vacuum angle . The ramifications of this
freedom on the construction of one- and two-soliton solutions are discussed. We
find, e.g., that once the angle is fixed and we choose
as the physical quantity, then there are four different solitons (or kinks)
connecting the vacuum angles , (defined modulo
). The most interesting result is the existence of a ``ghost'' soliton; it
goes over to the vacuum in isolation, but interacts with ``normal'' solitons by
giving them a finite phase shift.Comment: 9 pages in Latex + 3 figures (not included
A Characterization of Discrete Time Soliton Equations
We propose a method to characterize discrete time evolution equations, which
generalize discrete time soliton equations, including the -difference
Painlev\'e IV equations discussed recently by Kajiwara, Noumi and Yamada.Comment: 13 page
M\"obius Symmetry of Discrete Time Soliton Equations
We have proposed, in our previous papers, a method to characterize integrable
discrete soliton equations. In this paper we generalize the method further and
obtain a -difference Toda equation, from which we can derive various
-difference soliton equations by reductions.Comment: 21 pages, 4 figure, epsfig.st
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
Multilinear Operators: The Natural Extension Of Hirota's Bilinear Formalism
We introduce multilinear operators, that generalize Hirota's bilinear
operator, based on the principle of gauge invariance of the functions.
We show that these operators can be constructed systematically using the
bilinear 's as building blocks. We concentrate in particular on the
trilinear case and study the possible integrability of equations with one
dependent variable. The 5th order equation of the Lax-hierarchy as well as
Satsuma's lowest-order gauge invariant equation are shown to have simple
trilinear expressions. The formalism can be extended to an arbitrary degree of
multilinearity.Comment: 9 pages in plain Te
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
Multiple addition theorem for discrete and continuous nonlinear problems
The addition relation for the Riemann theta functions and for its limits,
which lead to the appearance of exponential functions in soliton type equations
is discussed. The presented form of addition property resolves itself to the
factorization of N-tuple product of the shifted functions and it seems to be
useful for analysis of soliton type continuous and discrete processes in the
N+1 space-time. A close relation with the natural generalization of bi- and
tri-linear operators into multiple linear operators concludes the paper.Comment: 9 page
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
Exact shock solution of a coupled system of delay differential equations: a car-following model
In this paper, we present exact shock solutions of a coupled system of delay
differential equations, which was introduced as a traffic-flow model called
{\it the car-following model}. We use the Hirota method, originally developed
in order to solve soliton equations. %While, with a periodic boundary
condition, this system has % a traveling-wave solution given by elliptic
functions. The relevant delay differential equations have been known to allow
exact solutions expressed by elliptic functions with a periodic boundary
conditions. In the present work, however, shock solutions are obtained with
open boundary, representing the stationary propagation of a traffic jam.Comment: 6 pages, 2 figure
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