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Exactly Solvable and Integrable Systems papers — page 12

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Hypercomplex Integrable Systems
In this paper we study hypercomplex manifolds in four dimensions. Rather than using an approach based on differential forms, we develop a dual approach using vector fields. The condition on these…
J. D. E. Grant, I. A. B. StrachanAug 27, 1998
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On Explicit Parametrisation of Spectral Curves for Moser-Calogero Particles and its Applications
The system of N classical particles on the line with the Weierstrass function as potential is known to be completely integrable. Recently D'Hoker and Phong found a beautiful…
K. L. VaninskyAug 27, 1998
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On Some One-Parameter Families of Three-Body Problems in One Dimension: Exchange Operator Formalism in Polar Coordinates and Scattering Properties
We apply the exchange operator formalism in polar coordinates to a one-parameter family of three-body problems in one dimension and prove the integrability of the model both with and without the…
Avinash Khare, C. QuesneAug 26, 1998
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Legendre transformations on the triangular lattice
The main purpose of the paper is to demonstrate that condition of invariance with respect to the Legendre transformations allows effectively isolate the class of integrable difference equations on…
V. E. AdlerAug 26, 1998
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Inversion of the linearized Korteweg-deVries equation at the multi-soliton solutions
Uniform estimates for the decay structure of the n-soliton solution of the Korteweg-deVries equation are obtained. The KdV equation, linearized at the n-soliton solution is investigated in a…
M. Haragus-Courcelle, D. H. SattingerAug 24, 1998
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On the Solution of a Painlevé III Equation
In a 1977 paper of McCoy, Tracy and Wu there appeared for the first time the solution of a Painlevé equation in terms of Fredholm determinants of integral operators. This equation is…
Harold WidomAug 24, 1998
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On fusion algebra of chiral SU(N)k models
We discuss some algebraic setting of chiral SU(N)k models in terms of the statistical dimensions of their fields. In particular, the conformal dimensions and the central charge of the chiral…
A. Lima-SantosAug 24, 1998
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On The KMS Condition for the critical Ising model
Using the KMS condition and exchange algebras we discuss the monodromy and modular properties of two-point KMS states of the critical Ising model.
A. Lima-Santos, Wagner UtielAug 24, 1998
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Localized solitons of hyperbolic su(N) AKNS system
Using the nonlinear constraint and Darboux transformation methods, the (m1,...,mN) localized solitons of the hyperbolic su(N) AKNS system are constructed. Here "hyperbolic su(N)" means that…
Zixiang ZhouAug 24, 1998
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Binary Nonlinearization of AKNS Spectral Problem under Higher-Order Symmetry Constraints
Binary nonlinearization of AKNS spectral problem is extended to the cases of higher-order symmetry constraints. The Hamiltonian structures, Lax representations, r-matrices and integrals of motion…
Yishen Li, Wen-Xiu MaAug 20, 1998
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The construction of Frobenius manifolds from KP tau-functions
Frobenius manifolds (solutions of WDVV equations) in canonical coordinates are determined by the system of Darboux-Egoroff equations. This system of partial differential equations appears as a…
J. W. van de Leur, R. MartiniAug 18, 1998
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Darboux transformations for twisted so(p,q) system and local isometric immersion of space forms
For the n-dimensional integrable system with a twisted so(p,q) reduction, Darboux transformations given by Darboux matrices of degree 2 are constructed explicitly. These Darboux transformations are…
Zixiang ZhouAug 17, 1998
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An Approach to Master Symmetries of Lattice Equations
An approach to master symmetries of lattice equations is proposed by the use of discrete zero curvature equation. Its key is to generate non-isospectral flows from the discrete spectral problem…
Benno Fuchssteiner, Wen-Xiu MaAug 14, 1998
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Relationship Between the Energy Eigenstates of Calogero-Sutherland Models With Oscillator and Coulomb-like Potentials
We establish a simple algebraic relationship between the energy eigenstates of the rational Calogero-Sutherland model with harmonic oscillator and Coulomb-like potentials. We show that there is an…
Pijush K. Ghosh, Avinash KhareAug 13, 1998
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Berezinian Construction of Super-Solitons in Supersymmetric Constrained KP Hierarchies
We consider a broad class of consistently reduced Manin-Radul supersymmetric KP hierarchies (MR-SKP) which are supersymmetric analogs of the ordinary bosonic constrained KP models. Compatibility of…
H. Aratyn, E. Nissimov, S. PachevaAug 5, 1998
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From One-Component KP Hierarchy to Two-Component KP Hierarchy and Back
We show that the system of the standard one-component KP hierarchy endowed with a special infinite set of abelian additional symmetries, generated by squared eigenfunction potentials, is equivalent…
H. Aratyn, E. Nissimov, S. PachevaAug 5, 1998
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Polynomial rings of the chiral SU(N)2 models
Via explicit diagonalization of the chiral SU(N)2 fusion matrices, we discuss the possibility of representing the fusion ring of the chiral SU(N) models, at level K=2, by a polynomial ring in a…
A. Lima-SantosAug 4, 1998
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An(1) Toda Solitons: a Relation between Dressing transformations and Vertex Operators
Affine Toda equations based on simple Lie algebras arise by imposing zero curvature condition on a Lax connection which belongs to the corresponding loop Lie algebra in the principal gradation. In…
H. Belich, R. PaunovAug 3, 1998
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Non-classical symmetries and the singular manifold method: A further two examples
This paper discusses two equations with the conditional Painleve property. The usefulness of the singular manifold method as a tool for determining the non-classical symmetries that reduce the…
Pilar G. Estevez, Pilar R. GordoaJul 27, 1998
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Separation of Variables in the Elliptic Gaudin Model
For the elliptic Gaudin model (a degenerate case of XYZ integrable spin chain) a separation of variables is constructed in the classical case. The corresponding separated coordinates are obtained as…
Evgueni K. Sklyanin, Takashi TakebeJul 23, 1998
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On the integrability of nonlinear partial differential equations
We investigate the integrability of Nonlinear Partial Differential Equations (NPDEs). The concepts are developed by firstly discussing the integrability of the KdV equation. We proceed by…
H. J. S. DorrenJul 22, 1998
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Dubrovin equations and integrable systems on hyperelliptic curves
We introduce the most general version of Dubrovin-type equations for divisors on a hyperelliptic curve of arbitrary genus, and provide a new argument for linearizing the corresponding completely…
F. Gesztesy, H. HoldenJul 14, 1998
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'Universality' of the Ablowitz-Ladik hierarchy
The aim of this paper is to summarize some recently obtained relations between the Ablowitz-Ladik hierarchy (ALH) and other integrable equations. It has been shown that solutions of finite subsystems…
V. E. VekslerchikJul 10, 1998
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Degenerate Frobenius manifolds and the bi-Hamiltonian structure of rational Lax equations
The bi-Hamiltonian structure of certain multi-component integrable systems, generalizations of the dispersionless Toda hierarchy, is studies for systems derived from a rational Lax function. One…
I. A. B. StrachanJul 8, 1998
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Extending Hamiltonian Operators to Get Bi-Hamiltonian Coupled KdV Systems
An analysis of extension of Hamiltonian operators from lower order to higher order of matrix paves a way for constructing Hamiltonian pairs which may result in hereditary operators. Based on a…
Wen-Xiu Ma, Maxim PavlovJul 8, 1998
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