5,408 research outputs found
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
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
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
Toda Lattice and Tomimatsu-Sato Solutions
We discuss an analytic proof of a conjecture (Nakamura) that solutions of
Toda molecule equation give those of Ernst equation giving Tomimatsu-Sato
solutions of Einstein equation. Using Pfaffian identities it is shown for Weyl
solutions completely and for generic cases partially.Comment: LaTeX 8 page
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
Two-dimensional soliton cellular automaton of deautonomized Toda-type
A deautonomized version of the two-dimensional Toda lattice equation is
presented. Its ultra-discrete analogue and soliton solutions are also
discussed.Comment: 11 pages, LaTeX fil
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
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
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
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