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Exactly Solvable and Integrable Systems papers — page 22

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On Adomian's Decomposition Method for Solving Differential Equations
We show that with a few modifications the Adomian's method for solving second order differential equations can be used to obtain the known results of the special functions of mathematical…
Petre Dita, Nicolae GramaMay 14, 1997
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Constructing Integrable Third Order Systems:The Gambier Approach
We present a systematic construction of integrable third order systems based on the coupling of an integrable second order equation and a Riccati equation. This approach is the extension of the…
Stephane Lafortune, Basil Grammaticos, Alfred RamaniMay 12, 1997
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Investigation of dynamical systems using tools of the theory of invariants and projective geometry
The investigation of nonlinear dynamical systems of the type x=P(x,y,z),y=Q(x,y,z),z=R(x,y,z) by means of reduction to some ordinary differential equations of the second order in…
L. A. Bordag, V. S. DryumaMay 7, 1997
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Some eigenstates for a model associated with solutions of tetrahedron equation. V. Two cases of string superposition
In paper IV (solv-int/9704013) we have considered a string living in the infinite lattice that was, in a sense, generated by a "particle". Here we show how to construct multi-string…
I. G. KorepanovMay 6, 1997
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On superintegrable systems closed to geodesic motion
In this work we consider superintegrable systems in the classical r-matrix method. By using other authomorphisms of the loop algebras we construct new superintegrable systems with rational…
A. V. TsiganovMay 6, 1997
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On equation of geodesic deviation and its solutions
Equations of geodesic deviation for the 3-dimensional and 4-dimensional Riemann spaces are discussed. Availability of wide classes of exact solutions of such equations, due to recent results for the…
V. S. Dryuma, B. G. KonopelchenkoMay 2, 1997
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Rational solutions to d-PIV
We study the rational solutions of the discrete version of Painleve's fourth equation d-PIV. The solutions are generated by applying Schlesinger transformations on the seed solutions -2z and…
Jarmo Hietarinta, Kenji KajiwaraMay 1, 1997
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Hamiltonian structure and coset construction of the supersymmetric extensions of N=2 KdV hierarchy
A manifestly N=2 supersymmetric coset formalism is applied to analyse the "fermionic" extensions of N=2 a=4 and a=-2 KdV hierarchies. Both these hierarchies can be obtained from a…
L. Bonora, S. KrivonosApr 29, 1997
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Computation of conserved densities for systems of nonlinear differential-difference equations
A new method for the computation of conserved densities of nonlinear differential-difference equations is applied to Toda lattices and discretizations of the Korteweg-de Vries and nonlinear…
Unal Goktas, Willy Hereman, Grant ErdmannApr 23, 1997
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Fusion rules for Quantum Transfer Matrices as a Dynamical System on Grassmann Manifolds
We show that the set of transfer matrices of an arbitrary fusion type for an integrable quantum model obey these bilinear functional relations, which are identified with an integrable dynamical…
O. Lipan, P. B. Wiegmann, A. ZabrodinApr 22, 1997
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Trilinear representation and the Moutard transformation for the Tzitzeica equation
In the paper we present a trilinear form and a Darboux-type transformation to an equation considered by Tzitzeica in 1910. This equation equivalent to the Bullough-Dodd-Jiber-Shabat equation. Soliton…
O. V. Kaptsov, Yu. V. Shan'koApr 21, 1997
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Some eigenstates for a model associated with solutions of tetrahedron equation. IV. String-particle marriage
This paper continues the series begun with works solv-int/9701016, solv-int/9702004 and solv-int/9703010. Here we construct more sophisticated strings, combining ideas from those papers and some…
I. G. KorepanovApr 19, 1997
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Huygens' Principle in Minkowski Spaces and Soliton Solutions of the Korteweg-de Vries Equation
A new class of linear second order hyperbolic partial differential operators satisfying Huygens' principle in Minkowski spaces is presented. The construction reveals a direct connection between…
Y. Berest, I. LoutsenkoApr 18, 1997
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Non-commutative and commutative integrability of generic Toda flows in simple Lie algebras
In this paper we prove the complete integrability of Toda flows on generic coadjoint orbits in simple Lie algebras.
M. Gekhtman, M. ShapiroApr 17, 1997
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Singularity analysis towards nonintegrability of nonhomogeneous nonlinear lattices
We show non-integrability of the nonlinear lattice of Fermi-Pasta-Ulam type via the singularity analysis(Picard-Vessiot theory) of normal variational equations of Lamé type.
Ken UmenoApr 16, 1997
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Krichever Maps, Faa' di Bruno Polynomials, and Cohomology in KP Theory
We study the geometrical meaning of the Faa' di Bruno polynomials in the context of KP theory. They provide a basis in a subspace W of the universal Grassmannian associated to the KP hierarchy.…
Gregorio Falqui, Cesare Reina, Alessandro ZampaApr 15, 1997
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Spectral Curves and Whitham Equations in Isomonodromic Problems of Schlesinger Type
It has been known since the beginning of this century that isomonodromic problems --- typically the Painlevé transcendents --- in a suitable asymptotic region look like a kind of…
Kanehisa TakasakiApr 8, 1997
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Dual Resonance Model Solves the Yang-Baxter Equation
The duality of dual resonance models is shown to imply that the four point string correlation function solves the Yang-Baxter equation. A reduction of transfer matrices to Al symmetry is described…
Satoru SaitoApr 6, 1997
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The Correspondence between Discrete Surface and Difference Geometry of the KP-hierarchy
The correspondence between two geometrical descriptions of the KP-hierarchy, one by discrete surface and another by difference analogue of differential geometry, is given.
Satoru SaitoApr 6, 1997
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A (2+1) dimensional integrable spin model: Geometrical and gauge equivalent counterpart, solitons and localized coherent structures
A non-isospectral (2+1) dimensional integrable spin equation is investigated. It is shown that its geometrical and gauge equivalent counterparts is the (2+1) dimensional nonlinear Schrödinger…
R. Myrzakulov, S. Vijayalakshmi, G. N. Nugmanova et al.Apr 6, 1997
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Complex Analysis of a Piece of Toda Lattice
We study a small piece of two dimensional Toda lattice as a complex dynamical system. In particular the Julia set, which appears when the piece is deformed, is shown analytically how it disappears as…
Satoru Saito, Noriko Saitoh, Hisao Konuma et al.Apr 5, 1997
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Convergent Normal Forms of Symmetric Dynamical Systems
It is shown that the presence of Lie-point-symmetries of (non-Hamiltonian) dynamical systems can ensure the convergence of the coordinate transformations which take the dynamical sytem (or vector…
G. CicognaApr 2, 1997
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Extended matrix Gelfand-Dickey hierarchies: reduction to classical Lie algebras
The Drinfeld-Sokolov reduction method has been used to associate with gln extensions of the matrix r-KdV system. Reductions of these systems to the fixed point sets of involutive Poisson maps,…
Laszlo Feher, Ian MarshallMar 31, 1997
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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…
A. ZabrodinMar 30, 1997
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WDVV and DZM
We show how the WDVV equations and the DZM system can be characterized via a background family of functions.
Robert CarrollMar 25, 1997
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