Riemannian Manifolds with Diagonal Metric. The Lamé and Bourlet SystemsWe discuss a Lie algebraic and differential geometry construction of solutions to some multidimensional nonlinear integrable systems describing diagonal metrics on Riemannian manifolds, in particular…A. V. Razumov, M. V. Saveliev·Dec 8, 1996SaveLearn
Correlators of the phase modelWe introduce the phase model on a lattice and solve it using the algebraic Bethe ansatz. Time-dependent temperature correlation functions of phase operators and the "darkness formation…N. M. Bogoliubov, A. G. Izergin, N. A. Kitanine·Dec 4, 1996SaveLearn
Solutions of (2+1)-dimensional spin systemsWe use the methods of group theory to reduce the equations of motion of two spin systems in (2+1) dimensions to sets of coupled ordinary differential equations. We present solutions of some classes…Z. Thomova, P. Winternitz, W. J. Zakrzewski·Dec 4, 1996SaveLearn
Representations of Two-Colour BWM Algebras and Solvable Lattice ModelsMany of the known solutions of the Yang-Baxter equation, which are related to solvable lattice models of vertex- and IRF-type, yield representations of the Birman-Wenzl-Murakami algebra. From these,…Uwe Grimm·Dec 3, 1996SaveLearn
The conservation of the Hamiltonian structures in Whitham's method of averagingThe work is devoted to the proof of the conservation of local field-theoretical Hamiltonian structures in Whitham's method of averaging. The consideration is based on the procedure of averaging…A. Ya. Maltsev·Nov 28, 1996SaveLearn
The L-Matrix for the Massive Thirring ModelAs the new results for the massive Thirring model the L-matrix and the algebraic relations for its action angle variables are given. So it is shown most directly that this model which describes…Y. -K. Zhou, K. D. Schotte·Nov 26, 1996SaveLearn
The orthogonal eigenbasis and norms of eigenvectors in the Spin Calogero-Sutherland ModelUsing a technique based on the Yangian Gelfand-Zetlin algebra and the associated Yangian Gelfand-Zetlin bases we construct an orthogonal basis of eigenvectors in the Calogero-Sutherland Model with…Kouichi Takemura, Denis Uglov·Nov 21, 1996SaveLearn
On the integrability of the square-triangle random tiling modelIt is shown that the square-triangle random tiling model is equivalent to an asymmetric limit of the three colouring model on the honeycomb lattice. The latter model is known to be the O(n) model at…Jan de Gier, Bernard Nienhuis·Nov 7, 1996SaveLearn
Spinless Calogero-Sutherland model with twisted boundary conditionIn this work, the spinless Calogero-Sutherland model with twisted boundary condition is studied. The ground state wavefunctions, the ground state energies, the full energy spectrum are provided in…D. F. Wang·Nov 6, 1996SaveLearn
Small-amplitude excitations in a deformable discrete nonlinear Schroedinger equationA detailed analysis of the small-amplitude solutions of a deformed discrete nonlinear Schrödinger equation is performed. For generic deformations the system possesses "singular" points which…V. V. Konotop, M. Salerno·Nov 4, 1996SaveLearn
The Coalescence Limit of the Second PainlevÉ EquationIn this paper, we study a well known asymptotic limit in which the second Painlevé equation (PII) becomes the first Painlevé equation (PI). The limit preserves the Painlevé property (i.e. that all…Rod Halburd, Nalini Joshi·Nov 4, 1996SaveLearn
Some explicit solutions of the Lamé and Bourlet type equationsSome special solutions to the multidimensional Lamé and Bourlet type equations are constructed in an explicit form.A. V. Razumov, M. V. Saveliev·Nov 1, 1996SaveLearn
Complex Blow-Up in Burgers' Equation: an Iterative ApproachWe show that for a given holomorphic noncharacteristic surface S in two-dimensional complex space, and a given holomorphic function on S, there exists a unique meromorphic solution of Burgers'…Nalini Joshi, Johannes A. Petersen·Oct 31, 1996SaveLearn
An orthogonal basis for the BN-type Calogero modelWe investigate algebraic structure for the BN-type Calogero model by using the exchange-operator formalism. We show that the set of the Jack polynomials whose arguments are Dunkl-type operators…Saburo Kakei·Oct 28, 1996SaveLearn
Integrabilities of the long range t-J model of twisted boundary conditionThe integrability of the one-dimensional long range supersymmetric t-J model has previously been established for both open systems and those closed by periodic boundary conditions through explicit…J. T. Liu, D. F. Wang·Oct 26, 1996SaveLearn
Solutions of Discretized Affine Toda Field Equations for An(1), Bn(1), Cn(1), Dn(1), An(2) and Dn+1(2)It is known that a family of transfer matrix functional equations, the T-system, can be compactly written in terms of the Cartan matrix of a simple Lie algebra. We formally replace this Cartan matrix…Zengo Tsuboi·Oct 25, 1996SaveLearn
The exact solution of an octagonal rectangle triangle random tilingWe present a detailed calculation of the recently published exact solution of a random tiling model possessing an eight-fold symmetric phase. The solution is obtained using Bethe Ansatz and provides…Jan de Gier, Bernard Nienhuis·Oct 22, 1996SaveLearn
Lax Representations and Zero Curvature Representations by Kronecker ProductIt is showed that Kronecker product can be applied to construct not only new Lax representations but also new zero curvature representations of integrable models. Meantime a different characteristic…Wen-Xiu Ma, Fu-Kui Guo·Oct 18, 1996SaveLearn
A new method to test discrete Painlevé equationsNecessary discretization rules to preserve the Painlevé property are stated. A new method is added to the discrete Painlevé test, which perturbs the continuous limit and generates infinitely many…R. Conte, M. Musette·Oct 9, 1996SaveLearn
On the solution of normality equations for the dimension n≥ 3The normality equations for the Newtonian dynamical systems on an arbitrary Riemannian manifold of the dimension n ≥ 3 are considered. Locally the solution of such equations reduces to three…Andrey Yu. Boldin, Ruslan A. Sharipov·Oct 9, 1996SaveLearn
Bilinearization of Discrete Soliton Equations and Singularity ConfinementBilinear forms for some nonlinear partial difference equations(discrete soliton equations) are derived based on the results of singularity confinement. Using the bilinear forms, the N-soliton and…K. Maruno, K. Kajiwara, S. Nakao et al.·Oct 8, 1996SaveLearn
Contractions of Integrable EquationsThe contraction is applied to obtaining of integrable systems associated with nonsemisimple algebras. The effect of contraction is splitting off some components from initial system without loss of…N. A. Gromov, I. V. Kostyakov, V. V. Kuratov·Oct 8, 1996SaveLearn
Automorphisms of sl(2) and dynamical r-matricesTwo outer automorphisms of infinite-dimensional representations of sl(2) algebra are considered. The similar constructions for the loop algebras and yangians are presented. The corresponding linear…A. V. Tsiganov·Oct 4, 1996SaveLearn
Darboux Coverings and Rational Reductions of the KP HierarchyWe use the method of Darboux coverings to discuss the invariant submanifolds of the KP equations, presented as conservation laws in the space of monic Laurent series in the spectral parameter (the…Paolo Casati, Gregorio Falqui, Franco Magri et al.·Oct 1, 1996SaveLearn
Nonlocal quadratic Poisson algebras, monodromy map, and Bogoyavlensky latticesA new Lax representation for the Bogoyavlensky lattice is found, its r--matrix interpretation is elaborated. The r--matrix structure turns out to be related to a highly nonlocal quadratic Poisson…Yuri B. Suris·Sep 30, 1996SaveLearn