1,637 research outputs found
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
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
Casorati Determinant Solution for the Relativistic Toda Lattice Equation
The relativistic Toda lattice equation is decomposed into three Toda systems,
the Toda lattice itself, B\"acklund transformation of Toda lattice and discrete
time Toda lattice. It is shown that the solutions of the equation are given in
terms of the Casorati determinant. By using the Casoratian technique, the
bilinear equations of Toda systems are reduced to the Laplace expansion form
for determinants. The -soliton solution is explicitly constructed in the
form of the Casorati determinant.Comment: 19 pages in plain Te
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
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
Crystal-field-induced magnetostrictions in the spin reorientation process of NdFeB-type compounds
Volume expansion associated with the spin reorientation
process of NdFeB-type compounds has been investigated in terms of
simple crystalline-electric-field (CEF) model. In this system,
is shown to be a direct measure of second order CEF energy. Calculated
anomalies in associated with the first-order magnetization
process of NdFeB are presented, which well reproduced the
observations.Comment: 2 pages, 2 figures, to appear in J. Magn. Magn. Mate
Bilinear Discrete Painleve-II and its Particular Solutions
By analogy to the continuous Painlev\'e II equation, we present particular
solutions of the discrete Painlev\'e II (d-P) equation. These
solutions are of rational and special function (Airy) type. Our analysis is
based on the bilinear formalism that allows us to obtain the function
for d-P. Two different forms of bilinear d-P are obtained
and we show that they can be related by a simple gauge transformation.Comment: 9 pages in plain Te
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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