Symmetric Linear Backlund Transformation for Discrete BKP and DKP equation

Proper lattices for the discrete BKP and the discrete DKP equaitons are determined. Linear B\"acklund transformation equations for the discrete BKP and the DKP equations are constructed, which possesses the lattice symmetries and generate auto-B\"acklund transformationsComment: 18 pages,3 figure

A Construction of Solutions to Reflection Equations for Interaction-Round-a-Face Models

We present a procedure in which known solutions to reflection equations for interaction-round-a-face lattice models are used to construct new solutions. The procedure is particularly well-suited to models which have a known fusion hierarchy and which are based on graphs containing a node of valency $1$. Among such models are the Andrews-Baxter-Forrester models, for which we construct reflection equation solutions for fixed and free boundary conditions.Comment: 9 pages, LaTe

Basic Representations of A_{2l}^(2) and D_{l+1}^(2) and the Polynomial Solutions to the Reduced BKP Hierarchies

Basic representations of A_{2l}^(2) and D_{l+1}^(2) are studied. The weight vectors are represented in terms of Schur's $Q$-functions. The method to get the polynomial solutions to the reduced BKP hierarchies is shown to be equivalent to a certain rule in Maya game.Comment: January 1994, 11 page

A Symmetric Generalization of Linear B\"acklund Transformation associated with the Hirota Bilinear Difference Equation

The Hirota bilinear difference equation is generalized to discrete space of arbitrary dimension. Solutions to the nonlinear difference equations can be obtained via B\"acklund transformation of the corresponding linear problems.Comment: Latex, 12 pages, 1 figur

QCD2-Screening, Confinement and Novel non-abelian Solutions

We analyze the question of screening versus confinement in bosonized massless QCD in two dimensions. We deduce the screening behavior of massless $SU(N_c)$ QCD with flavored fundamental fermions and fermions in the adjoint representation. This is done by computing the potential between external quarks as well as by bosonizing also the external sources and analyzing the states of the combined system. We write down novel "non-abelian Schwinger like" solutions of the equations of motion, compute their masses and argue that an exchange of massive modes of this type is associated with the screening mechanism.Comment: 25 pages,TeX,phyzzx. A reference was adde

Two-component Analogue of Two-dimensional Long Wave-Short Wave Resonance Interaction Equations: A Derivation and Solutions

The two-component analogue of two-dimensional long wave-short wave resonance interaction equations is derived in a physical setting. Wronskian solutions of the integrable two-component analogue of two-dimensional long wave-short wave resonance interaction equations are presented.Comment: 16 pages, 9 figures, revised version; The pdf file including all figures: http://www.math.utpa.edu/kmaruno/yajima.pd

B\"{a}cklund transformations for the constrained dispersionless hierarchies and dispersionless hierarchies with self-consistent sources

The B\"{a}cklund transformations between the constrained dispersionless KP hierarchy (cdKPH) and the constrained dispersionless mKP hieararchy (cdmKPH) and between the dispersionless KP hieararchy with self-consistent sources (dKPHSCS) and the dispersionless mKP hieararchy with self-consistent sources (dmKPHSCS) are constructed. The auto-B\"{a}cklund transformations for the cdmKPH and for the dmKPHSCS are also formulated.Comment: 11 page

The spectrum of states with one current acting on the adjoint vacuum of massless QCD2

We consider a ``one current'' state, which is obtained by the application of a color current on the ``adjoint'' vacuum. This is done in $QCD_2$, with the underlying quarks in the fundamental representation. The quarks are taken to be massless, in which case the theory on the light-front can be ``currentized'', namely, formulated in terms of currents only. The adjoint vacuum is shown to be the application of a current derivative, at zero momentum, on the singlet vacuum. We apply the operator $M^2=2P^+P^-$ on these states and find that in general they are not eigenstates of $M^2$ apart from the large $N_f$ limit. Problems with infra-red regularizations are pointed out. We discuss the fermionic structure of these states.Comment: 18 pages, no figures. v2: minor corrections. v3: added some clarifications and remarks, mainly on the contribution of zero modes. Typos corrected, references added. To appear in Nuclear Physics

A survey of Hirota's difference equations

A review of selected topics in Hirota's bilinear difference equation (HBDE) is given. This famous 3-dimensional difference equation is known to provide a canonical integrable discretization for most important types of soliton equations. Similarly to the continuous theory, HBDE is a member of an infinite hierarchy. The central point of our exposition is a discrete version of the zero curvature condition explicitly written in the form of discrete Zakharov-Shabat equations for M-operators realized as difference or pseudo-difference operators. A unified approach to various types of M-operators and zero curvature representations is suggested. Different reductions of HBDE to 2-dimensional equations are considered. Among them discrete counterparts of the KdV, sine-Gordon, Toda chain, relativistic Toda chain and other typical examples are discussed in detail.Comment: LaTeX, 43 pages, LaTeX figures (with emlines2.sty

Generalized Darboux transformations for the KP equation with self-consistent sources

The KP equation with self-consistent sources (KPESCS) is treated in the framework of the constrained KP equation. This offers a natural way to obtain the Lax representation for the KPESCS. Based on the conjugate Lax pairs, we construct the generalized binary Darboux transformation with arbitrary functions in time $t$ for the KPESCS which, in contrast with the binary Darboux transformation of the KP equation, provides a non-auto-B\"{a}cklund transformation between two KPESCSs with different degrees. The formula for N-times repeated generalized binary Darboux transformation is proposed and enables us to find the N-soliton solution and lump solution as well as some other solutions of the KPESCS.Comment: 20 pages, no figure