Commuting Charges of the Quantum Korteweg-deVries and Boussinesq Theories from the Reduction of W(infinity) and W(1+infinity) AlgebrasIntegrability of the quantum Boussinesq equation for c=-2 is demonstrated by giving a recursive algorithm for generating explicit expressions for the infinite number of commuting charges based on a…Andrew J. Bordner·Nov 27, 1997SaveLearn
Coset approach to the N=2 supersymmetric matrix GNLS hierarchiesWe discuss a large class of coset constructions of the N=2 sl(n|n-1) affine superalgebra. We select admissible subalgebras, i.e. subalgebras that induce linear chiral/antichiral constraints on the…L. Bonora, S. Krivonos, A. Sorin·Nov 20, 1997SaveLearn
Vertex Operators and Solitons of Constrained KP HierarchiesWe construct the vertex operator representation for the Affine Kac-Moody SL(M+K+1) algebra, which is relevant for the construction of the soliton solutions of the constrained KP hierarchies. The…H. Aratyn, L. A. Ferreira, J. F. Gomes et al.·Nov 20, 1997SaveLearn
The N=2 supersymmetric matrix GNLS hierarchiesWe construct the matrix generalization of the N=2 supersymmetric GNLS hierarchies. This is done by exhibiting the corresponding matrix super Lax operators in terms of N=2 superfields in two different…L. Bonora, S. Krivonos, A. Sorin·Nov 20, 1997SaveLearn
Few remarks on Baecklund transformations for many-body systemsUsing the n-particle periodic Toda lattice and the relativistic generalization due to Ruijsenaars of the elliptic Calogero-Moser system as examples, we revise the basic properties of the Baecklund…V. B. Kuznetsov, E. K. Sklyanin·Nov 14, 1997SaveLearn
The nondynamical r-matrix structure of the elliptic Calogero-Moser modelIn this paper, we construct a new Lax operator for the elliptic Calogero-Moser model with N=2. The nondynamical r-matrix structure of this Lax operator is also studied . The relation between our Lax…Bo-yu Hou, Wen-li Yang·Nov 12, 1997SaveLearn
A new class of completely integrable quantum spin chainsA large (infinitely-dimensional) class of completely integrable (possibly non-autonomous) spin chains is discovered associated to an infinite-dimensional Lie Algebra of infinite rank. The complete…Tomaz Prosen·Nov 10, 1997SaveLearn
Comment on ``Equal-time temperature correlators of the one-dimensional Heisenberg XY chain'', preprint solv-int/9710028In the comment we give references to our papers where the problem was solved for more general case of time-dependent finite temperature correlators.Kirill Ilinski, Alexander Stepanenko·Nov 6, 1997SaveLearn
A Note on the Gauge Equivalence between the Manin-Radul and Laberge-Mathieu Super KdV HierarchiesThe gauge equivalence between the Manin-Radul and Laberge-Mathieu super KdV hierarchies is revisited. Apart from the Inami-Kanno transformation, we show that there is another gauge transformation…Jiin-Chang Shaw, Ming-Hsien Tu·Nov 5, 1997SaveLearn
On the Integrability of the One-Dimensional Open XYZ Spin ChainThe Lax pair for the one-dimensional open XYZ spin chain is constructed, this shows that the system is completely integrable .Guo-xing Ju, Chi Xiong·Nov 4, 1997SaveLearn
Surfaces of Revolution via the Schroedinger Equation : Construction, Integrable Dynamics and VisualizationSurfaces of revolution in three-dimensional Euclidean space are considered. Several new examples of surfaces of revolution associated with well-known solvable cases of the Schoedinger equation…R. Beutler, B. G. Konopelchenko·Nov 3, 1997SaveLearn
Additional symmetries of the Zakharov-Shabat hierarchy, String equation and IsomonodromyIsomonodromic deformations are nothing but symmetries of the Zakharov-Shabat (isospectral) hierarchy, both the basic ones (belonging to the hierarchy) and additional, restricted to the submanifold of…L. A. Dickey·Oct 31, 1997SaveLearn
Darboux Transformations for SUSY Integrable SystemsSeveral types of Darboux transformations for supersymmetric integrable systems such as the Manin-Radul KdV, Mathieu KdV and SUSY sine-Gordon equations are considered. We also present solutions such…Q. P. Liu, Manuel Manas·Oct 31, 1997SaveLearn
Integrable Models and the Higher Dimensional Representations of Graded Lie AlgebrasWe construct a zero curvature formulation, in superspace, for the sTB-B hierarchy which naturally reduces to the zero curvature condition in terms of components, thus solving one of the puzzling…J. C. Brunelli, Ashok Das·Oct 31, 1997SaveLearn
Equal-time temperature correlators of the one-dimensional Heisenberg XY chainRepresentations as determinants of M× M dimensional matrices are obtained for equal-time temperature correlators of the anisotropic Heisenberg XY chain. These representations are simple…A. G. Izergin, V. S. Kapitonov, N. A. Kitanine·Oct 30, 1997SaveLearn
The sAKNS HierarchyWe study, systematically, the properties of the supersymmetric AKNS (sAKNS) hierarchy. In particular, we discuss the Lax representation in terms of a bosonic Lax operator and some special features of…Henrik Aratyn, Ashok Das·Oct 28, 1997SaveLearn
Self-duality of the SL2 Hitchin integrable system at genus twoWe revisit the Hitchin integrable system whose phase space is the bundle cotangent to the moduli space N of holomorphic SL2-bundles over a smooth complex curve of genus two. N may be…Krzysztof Gawedzki, Pascal Tran-Ngoc-Bich·Oct 27, 1997SaveLearn
Complete Nondiagonal Reflection Matrices of RSOS/SOS and Hard Hexagon ModelsIn this paper we compute the most general nondiagonal reflection matrices of the RSOS/SOS models and hard hexagon model using the boundary Yang-Baxter equations. We find new one-parameter family of…C. Ahn, C. K. You·Oct 26, 1997SaveLearn
Analytic and Asymptotic Methods for Nonlinear Singularity Analysis: a Review and Extensions of Tests for the Painlevé PropertyThe integrability (solvability via an associated single-valued linear problem) of a differential equation is closely related to the singularity structure of its solutions. In particular, there is…Martin D. Kruskal, Nalini Joshi, Rod Halburd·Oct 25, 1997SaveLearn
The Second Painlevé Equation in the Large-Parameter Limit I: Local Asymptotic AnalysisIn this paper, we find all possible asymptotic behaviours of the solutions of the second Painlevé equation y''=2y3+xy +α as the parameter α∞ in the local region xα2/3. We…Nalini Joshi·Oct 24, 1997SaveLearn
The Discrete Painlevé I HierarchyThe discrete Painlevé I equation (dPI) is an integrable difference equation which has the classical first Painlevé equation (PI) as a continuum limit. dPI is believed to be…Clio Cresswell, Nalini Joshi·Oct 24, 1997SaveLearn
The Painlevé approach to nonlinear ordinary differential equationsThe ``Painlevé analysis'' is quite often perceived as a collection of tricks reserved to experts. The aim of this course is to demonstrate the contrary and to unveil the simplicity and the…R. Conte·Oct 24, 1997SaveLearn
Jack polynomials, generalized binomial coefficients and polynomial solutions of the generalized Laplace's equationWe discuss the symmetric homogeneous polynomial solutions of the generalized Laplace's equation which arises in the context of the Calogero-Sutherland model on a line. The solutions are expressed…S. Chaturvedi·Oct 23, 1997SaveLearn
D-modules and Darboux transformationsA method of G. Wilson for generating commutative algebras of ordinary differential operators is extended to higher dimensions. Our construction, based on the theory of D-modules, leads to a new class…Yu. Berest, A. Kasman·Oct 23, 1997SaveLearn
Unifying structures in quantum integrable systemsBasic concepts of quantum integrable systems (QIS) are presented stressing on the unifying structures underlying such diverse models. Variety of ultralocal and nonultralocal models is shown to be…Anjan Kundu·Oct 23, 1997SaveLearn