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Exactly Solvable and Integrable Systems papers — page 31

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Integrable Models on Hyper-Elliptic Surfaces
We present an elementary introduction to the construction of integrable models on hyper-elliptic surfaces for non specialists; also, we present some of the details of the paper `solv-int/9504002'…
Costas J. Efthimiou, Samwel A. ApikyanJul 12, 1995
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Fredholm determinants and the mKdV/sinh-Gordon hierarchies
For a particular class of integral operators K we show that the quantity \[:= (I+K)- (I-K)\] satisfies both the integrated mKdV hierarchy and the sinh-Gordon hierarchy. This…
Craig A. Tracy, Harold WidomJul 7, 1995
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Holomorphic Curves and Toda Systems
Geometry of holomorphic curves from point of view of open Toda systems is discussed. Parametrization of curves related this way to non-exceptional simple Lie algebras is given. This gives rise to…
Adam DoliwaJul 3, 1995
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Iso-spectral deformations of general matrix and their reductions on Lie algebras
We study an iso-spectral deformation of general matrix which is a natural generalization of the Toda lattice equation. We prove the integrability of the deformation, and give an explicit formula for…
Yuji Kodama, Jian YeJul 3, 1995
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Algebraic integrable dynamical systems, 2+1-dimensional models in wholly discrete space-time, and inhomogeneous models in 2-dimensional statistical physics
This paper is devoted to constructing and studying exactly solvable dynamical systems in discrete time obtained from some algebraic operations on matrices, to reductions of such systems leading to…
I. G. KorepanovJul 1, 1995
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Infinite-Dimensional Estabrook-Wahlquist Prolongations for the sine-Gordon Equation
We are looking for the universal covering algebra for all symmetries of a given pde, using the sine-Gordon equation as a typical example for a non-evolution equation. For non-evolution equations,…
J. D. Finley, III, John K. McIverJun 9, 1995
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Separation of Variables in BC-type Gaudin Magnet
The integrable system is introduced based on the Poisson rs -matrix structure. This is a generalization of the Gaudin magnet, and in SL(2) case isomorphic to the generalized Neumann model. The…
Kazuhiro HikamiJun 7, 1995
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Conditional Lie-Bäcklund symmetry and reduction of evolution equations.
We suggest a generalization of the notion of invariance of a given partial differential equation with respect to Lie-Bäcklund vector field. Such generalization proves to be effective and enables us…
R. Z. ZhdanovMay 31, 1995
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Approximate Lie Group Analysis of a Model Advection Equation on an Unstructured Grid
A technique of ``approximate group analysis'' recently developed by Baikov, Gazizov and Ibragimov is applied to a differential approximation (otherwise referred to as an equivalent…
Azat M. LatypovMay 30, 1995
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Toda Hierarchy with Indefinite Metric
We consider a generalization of the full symmetric Toda hierarchy where the matrix L of the Lax pair is given by L=LS, with a full symmetric matrix L and a nondegenerate…
Yuji Kodama, Jian YeMay 19, 1995
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Integrable boundary conditions for the Toda lattice
The problem of construction of the boundary conditions for the Toda lattice compatible with its higher symmetries is considered. It is demonstrated that this problem is reduced to finding of the…
V. E. Adler, I. T. HabibullinMay 17, 1995
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On the algebraic non-integrability of the Halphen system
It is proved that the Halphen system of ordinary differential equations has no non-trivial rational first integrals.
Andrzej J. ~Maciejewski, Jean-Marie StrelcynMay 12, 1995
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Topics in nonhamiltonian (magnetic-type) interaction of classical hamiltonian dynamical systems. I
A convenient algebraic structure to describe some forms of dynamics of two hamiltonian systems with nonpotential (magnetic--type) interaction is considered. An algebraic mechanism of generation of…
Denis V. JurievMay 5, 1995
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Painlevé Analysis and Exact Solutions of a Modified Boussinesq Equation
We consider a modified Boussinesq type equation. The Painlevé test of the WTC method is performed for this equation and it shows that the equation has weak Painlevé property. Some exact solutions are…
Q. P. LiuApr 27, 1995
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V(1,1)(t)-PERTURBED MODELS OF CFT AND THEIR QUANTUM GROUP SYMMETRY
We propose a new massive integrable model in quantum field theory. This model is obtained as a perturbed model of the minimal conformal field theories on the hyper-elliptic surfaces by a particular…
S. A. APIKYAN, C. J. EFTHIMIOUApr 5, 1995
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Separation of Variables. New Trends.
The review is based on the author's papers since 1985 in which a new approach to the separation of variables () has being developed. It is argued that , understood generally enough, could…
E. K. SklyaninApr 4, 1995
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On the dynamics of noncanonically coupled oscillators and its hidden superstructure
The classical and quantum dynamics of the noncanonically coupled oscillators is considered. It is shown that though the classical dynamics is well--defined for both harmonic and anharmonic…
Denis V. JurievMar 25, 1995
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Theory of Pump Depletion and Spike Formation in Stimulated Raman Scattering
By using the inverse spectral transform, the SRS equations are solved and the explicit output data is given for arbitrary laser pump and Stokes seed profiles injected on a vacuum of optical phonons.…
C. Claude, J. LeonMar 17, 1995
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Supersymmetric Harry Dym Type Equations
A supersymmetric version is proposed for the well known Harry Dym system. A general class super Lax operator which leads to consistent equations is considered.
Q. P. LiuMar 17, 1995
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Explicit Integration of the Full Symmetric Toda Hierarchy and the Sorting Property
We give an explicit formula for the solution to the initial value problem of the full symmetric Toda hierarchy. The formula is obtained by the orthogonalization procedure of Szegö, and is also…
Y. Kodama, K. T-R McLaughlinFeb 22, 1995
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On The Observability For Distributed Systems By Means Of Linear Operations
An observability problem for linear autonomous distributed systems in the class of linear operations is considered. A criterion of observability with respect to terminal state has been proved. A…
B. ShklyarFeb 16, 1995
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Isothermic surfaces in 3 as soliton surfaces
We show that the theory of isothermic surfaces in 3 -- one of the oldest branches of differential geometry -- can be reformulated within the modern theory of completely integrable (soliton)…
Jan Cieśliński, Piotr Goldstein, Antoni SymFeb 14, 1995
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The Hamiltonian structure of the dispersionless Toda hierarchy
The Hamiltonian structure of the two-dimensional dispersionless Toda hierarchy is studied, this being a particular example of a system of hydrodynamic type. The polynomial conservation laws for the…
D. B. Fairlie, I. A. B. StrachanFeb 13, 1995
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Discrete Toda Field Equations
There are two-dimensional Toda field equations corresponding to each (finite or affine) Lie algebra. The question addressed in this note is whether there exist integrable discrete versions of these.…
R. S. WardFeb 8, 1995
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Shock waves in the dissipative Toda lattice
We consider the propagation of a shock wave (SW) in the damped Toda lattice. The SW is a moving boundary between two semi-infinite lattice domains with different densities. A steadily moving SW may…
J. Hietarinta, T. Kuusela, B. MalomedFeb 3, 1995
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