6,811 research outputs found
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
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
Zn and Ni doping effects on the low-energy spin excitations in LaSrCuO
Impurity effects of Zn and Ni on the low-energy spin excitations were
systematically studied in optimally doped La1.85Sr0.15Cu1-yAyO4 (A=Zn, Ni) by
neutron scattering. Impurity-free La1.85Sr0.15CuO4 shows a spin gap of 4meV
below Tc in the antiferromagnetic(AF) incommensurate spin excitation. In
Zn:y=0.004, the spin excitation shows a spin gap of 3meV below Tc. In
Zn:y=0.008 and Zn:y=0.011, however, the magnetic signals at 3meV decrease below
Tc and increase again at lower temperature, indicating an in-gap state. In
Zn:y=0.017, the low-energy spin state remains unchanged with decreasing
temperature, and elastic magnetic peaks appear below 20K then exponentially
increase. As for Ni:y=0.009 and Ni:y=0.018, the low-energy excitations below
3meV and 2meV disappear below Tc. The temperature dependence at 3meV, however,
shows no upturn in constrast with Zn:y=0.008 and Zn:y=0.011, indicating the
absence of in-gap state. In Ni:y=0.029, the magnetic signals were observed also
at 0meV. Thus the spin gap closes with increasing Ni. Furthermore, as omega
increases, the magnetic peak width broadens and the peak position, i.e.
incommensurability, shifts toward the magnetic zone center (pi pi). We
interpret the impurity effects as follows: Zn locally makes a
non-superconducting island exhibiting the in-gap state in the superconducting
sea with the spin gap. Zn reduces the superconducting volume fraction, thus
suppressing Tc. On the other hand, Ni primarily affects the superconducting
sea, and the spin excitations become more dispersive and broaden with
increasing energy, which is recognized as a consequence of the reduction of
energy scale of spin excitations. We believe that the reduction of energy scale
is relevant to the suppression of Tc.Comment: 13pages, 14figures; submitted to Phys. Rev.
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
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 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
Spin Dynamical Properties of the Layered Perovskite La1.2Sr1.8Mn2O7
Inelastic neutron-scattering measurements were performed on a single crystal
of the layered colossal magnetoresistance (CMR) material La1.2Sr1.8Mn2O7 (Tc ~
120K). We found that the spin wave dispersion is almost perfectly
two-dimensional with the in-plane spin stiffness constant D ~ 151meVA. The
value is similar to that of similarly doped La1-xSrxMnO3 though its Tc is three
times higher, indicating a large renormalization due to low dimensionality.
There exist two branches due to a coupling between layers within a
double-layer. The out-of-plane coupling is about 30% of the in-plane coupling
though the Mn-O bond lengths are similar.Comment: 3 pages, 3 figures J. Phys. Chem. Solids in pres
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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