1,503 research outputs found
Projective reduction of the discrete Painlev\'e system of type
We consider the q-Painlev\'e III equation arising from the birational
representation of the affine Weyl group of type . We study
the reduction of the q-Painlev\'e III equation to the q-Painlev\'e II equation
from the viewpoint of affine Weyl group symmetry. In particular, the mechanism
of apparent inconsistency between the hypergeometric solutions to both
equations is clarified by using factorization of difference operators and the
functions.Comment: 27 pages, 10 figure
On a q-difference Painlev\'e III equation: II. Rational solutions
Rational solutions for a -difference analogue of the Painlev\'e III
equation are considered. A Determinant formula of Jacobi-Trudi type for the
solutions is constructed.Comment: Archive version is already official. Published by JNMP at
http://www.sm.luth.se/math/JNMP
A study on the fourth q-Painlev\'e equation
A q-difference analogue of the fourth Painlev\'e equation is proposed. Its
symmetry structure and some particular solutions are investigated.Comment: 18 page
Hypergeometric solutions to the q-Painlev\'e equation of type
We consider the q-Painlev\'e equation of type (a version of
q-Painlev\'e V equation) and construct a family of solutions expressible in
terms of certain basic hypergeometric series. We also present the determinant
formula for the solutions.Comment: 16 pages, IOP styl
Toda Lattice Hierarchy and Zamolodchikov's Conjecture
In this letter, we show that certain Fredholm determinant ,
introduced by Zamolodchikov in his study of 2D polymers, is a continuum limit
of soliton solution for the Toda lattice hierarchy with 2-periodic reduction
condition.Comment: 6 pages, LaTeX file, no figure
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
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
A remark on the Hankel determinant formula for solutions of the Toda equation
We consider the Hankel determinant formula of the functions of the
Toda equation. We present a relationship between the determinant formula and
the auxiliary linear problem, which is characterized by a compact formula for
the functions in the framework of the KP theory. Similar phenomena that
have been observed for the Painlev\'e II and IV equations are recovered. The
case of finite lattice is also discussed.Comment: 14 pages, IOP styl
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