986 research outputs found
Enhancement of the spin pumping efficiency by spin-wave mode selection
The spin pumping efficiency of lateral standing spin wave modes in a
rectangular YIG/Pt sample has been investigated by means of the inverse
spin-Hall effect (ISHE). The standing spin waves drive spin pumping, the
generation of spin currents from magnetization precession, into the Pt layer
which is converted into a detectable voltage due to the ISHE. We discovered
that the spin pumping efficiency is significantly higher for lateral standing
surface spin waves rather than for volume spin wave modes. The results suggest
that the use of higher-mode surface spin waves allows for the fabrication of an
efficient spin-current injector
On a q-difference Painlev\'e III equation: I. Derivation, symmetry and Riccati type solutions
A q-difference analogue of the Painlev\'e III equation is considered. Its
derivations, affine Weyl group symmetry, and two kinds of special function type
solutions are discussed.Comment: arxiv version is already officia
The discrete potential Boussinesq equation and its multisoliton solutions
An alternate form of discrete potential Boussinesq equation is proposed and
its multisoliton solutions are constructed. An ultradiscrete potential
Boussinesq equation is also obtained from the discrete potential Boussinesq
equation using the ultradiscretization technique. The detail of the
multisoliton solutions is discussed by using the reduction technique. The
lattice potential Boussinesq equation derived by Nijhoff et al. is also
investigated by using the singularity confinement test. The relation between
the proposed alternate discrete potential Boussinesq equation and the lattice
potential Boussinesq equation by Nijhoff et al. is clarified.Comment: 17 pages,To appear in Applicable Analysis, Special Issue of
Continuous and Discrete Integrable System
Rational solutions of the discrete time Toda lattice and the alternate discrete Painleve II equation
The Yablonskii-Vorob'ev polynomials , which are defined by a second
order bilinear differential-difference equation, provide rational solutions of
the Toda lattice. They are also polynomial tau-functions for the rational
solutions of the second Painlev\'{e} equation (). Here we define
two-variable polynomials on a lattice with spacing , by
considering rational solutions of the discrete time Toda lattice as introduced
by Suris. These polynomials are shown to have many properties that are
analogous to those of the Yablonskii-Vorob'ev polynomials, to which they reduce
when . They also provide rational solutions for a particular
discretisation of , namely the so called {\it alternate discrete}
, and this connection leads to an expression in terms of the Umemura
polynomials for the third Painlev\'{e} equation (). It is shown that
B\"{a}cklund transformation for the alternate discrete Painlev\'{e} equation is
a symplectic map, and the shift in time is also symplectic. Finally we present
a Lax pair for the alternate discrete , which recovers Jimbo and Miwa's
Lax pair for in the continuum limit .Comment: 23 pages, IOP style. Title changed, and connection with Umemura
polynomials adde
Finite-dimensional reductions of the discrete Toda chain
The problem of construction of integrable boundary conditions for the
discrete Toda chain is considered. The restricted chains for properly chosen
closure conditions are reduced to the well known discrete Painlev\'e equations
, , . Lax representations for these discrete
Painlev\'e equations are found.Comment: Submitted to Jornal of Physics A: Math. Gen., 14 page
Separation of colour degree of freedom from dynamics in a soliton cellular automaton
We present an algorithm to reduce the coloured box-ball system, a one
dimensional integrable cellular automaton described by motions of several
colour (kind) of balls, into a simpler monochrome system. This algorithm
extracts the colour degree of freedom of the automaton as a word which turns
out to be a conserved quantity of this dynamical system. It is based on the
theory of crystal basis and in particular on the tensor products of sl_n
crystals of symmetric and anti-symmetric tensor representations.Comment: 19 page
The group law on the tropical Hesse pencil
We show that the addition of points on the tropical Hesse curve can be
realized via the intersection with a tropical line. Then the addition formula
for the tropical Hesse curve is reduced from those for the level-three theta
functions through the ultradiscretization procedure. A tropical analogue of the
Hessian group, the group of linear automorphisms acting on the Hesse pencil, is
also investigated; it is shown that the dihedral group of degree three is the
group of linear automorphisms acting on the tropical Hesse pencil.Comment: 17 pages, 1 figure, submitted to Special Issue of the Journal
Mathematics and Computers in Simulation on "Nonlinear Waves: Computation and
Theory
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