We construct N-soliton solutions to the equation called Q3 in the recent Adler-Bobenko-Suris classification. An essential ingredient in the construction is the relationship of (Q3) δ=0 to the equation proposed by Nijhoff, Quispel and Capel in 1983 (the NQC equation). This latter equation has two extra parameters, and depending on their sign choices we get a 4-to-1 relationship from NQC to (Q3) ...

D-branes constitute an important part of the superstring theory in its nonperturbative description. Especially coincident multi D-brane states enable us to reproduce nonabelian guage theory in the low energy. From the mathematical point of view, on the other hand, a non-perturbative field theory must be formulated within the framework of a completely integrable system, namely a system whose who...

It is shown that the properties of the Gauss decomposition of quantum groups and the known Jimbo homomorphism permit us to realize these groups as subalgebras of well defined algebras constructed from generators of the corresponding undeformed Lie algebras. This research was supported by RFFI grants No 97-01-01152. E-mail adress: [email protected] 1. The purpose of this Letter is to show tha...

A q-analogue of the ĝl3 Drinfel’d-Sokolov hierarchy is proposed as a reduction of the q-KP hierarchy. Applying a similarity reduction and a q-Laplace transformation to the hierarchy, one can obtain the q-Painlevé VI equation proposed by Jimbo and Sakai. AMS classification scheme numbers: 37K10, 39A12, 39A13 Submitted to: J. Phys. A: Math. Gen. Dedicated to Professors Junkichi Satsuma and Basil ...

Kanji Hioka Graduate School of Science and Engineering, Yamaguchi University 1677-1 Yoshida, Yamaguchi 753-8512, Japan [email protected] Yoshimasa Miwa Graduate School of Science and Engineering, Yamaguchi University 1677-1 Yoshida, Yamaguchi 753-8512, Japan [email protected] Chen Li Human Genome Center, University of Tokyo 4-6-1 Shirokanedai, Minatoku, Tokyo 108-8639, Ja...

In the present paper, we are with integrable discretization of a modified Camassa–Holm (mCH) equation linear dispersion term. The key construction is semidiscrete analog for set bilinear equations mCH equation. First, show that these and their determinant solutions either in Gram-type or Casorati-type can be reduced from discrete Kadomtsev–Petviashvili (KP) through Miwa transformation. Then, by...

We present a framework for the study of q-differential equations satisfied by q-semi-classical orthogonal systems. As an example, we identify the q-differential equation satisfied by a deformed version of the little q-Jacobi polynomials as a guage transformation of a special case of the associated linear problem for q-PV I . We obtain a parametrization of the associated linear problem in terms ...

in the fundamental representation. Conspicuously absent from this list is A (1) n for n > 1. This is because in order to demonstrate integrability, we assume that the corresponding R matrix has crossing symmetry, which is not true in the case A (1) n for n > 1. Sklyanin has demonstrated that an integrable open spin chain can be constructed with an R matrix that satisfies nothing more than the Y...