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Exactly Solvable and Integrable Systems papers — page 9

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The Cole-Hopf and Miura transformations revisited
An elementary yet remarkable similarity between the Cole-Hopf transformation relating the Burgers and heat equation and Miura's transformation connecting the KdV and mKdV equations is studied in…
Fritz Gesztesy, Helge HoldenDec 21, 1998
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Discrete and Continuous Linearizable Equations
We study the projective systems in both continuous and discrete settings. These systems are linearizable by construction and thus, obviously, integrable. We show that in the continuous case it is…
S. Lafortune, B. Grammaticos, A. RamaniDec 21, 1998
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Hamiltonian structure of real Monge-Ampère equations
The real homogeneous Monge-Ampère equation in one space and one time dimensions admits infinitely many Hamiltonian operators and is completely integrable by Magri's theorem. This remarkable…
Y. NutkuDec 21, 1998
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Extension of the bilinear formalism to supersymmetric KdV-type equations
Extending the gauge-invariance principle for τfunctions of the standard bilinear formalism to the supersymmetric case, we define N=1 supersymmetric Hirota operators. Using them, we bilinearize SUSY…
A. S. CarsteaDec 21, 1998
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Spontaneous magnetization of the XXZ Heisenberg spin-1/2 chain
Determinant representations of form factors are used to represent the spontaneous magnetization of the Heisenberg XXZ chain (Delta >1) on the finite lattice as the ratio of two determinants. In the…
A. G. Izergin, N. Kitanine, J. M. Maillet et al.Dec 18, 1998
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Functional representation of the Ablowitz-Ladik hierarchy. II
In this paper I continue studies of the functional representation of the Ablowitz-Ladik hierarchy (ALH). Using formal series solutions of the zero-curvature condition I rederive the functional…
V. E. VekslerchikDec 18, 1998
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Symmetries of Discrete Dynamical Systems Involving Two Species
The Lie point symmetries of a coupled system of two nonlinear differential-difference equations are investigated. It is shown that in special cases the symmetry group can be infinite dimensional, in…
D. Gomez-Ullate, S. Lafortune, P. WinternitzDec 16, 1998
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Hamiltonian Structures of Generalized Manin-Radul Super KdV and Constrained Super KP Hierarchies
A study of Hamiltonian structures associated with supersymmetric Lax operators is presented. Following a constructive approach, the Hamiltonian structures of Inami-Kanno super KdV hierarchy and…
Ming-Hsien Tu, Jiin-Chang ShawDec 16, 1998
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Finite-dimensional analogs of string s <-> t duality and pentagon equation
We put forward one of the forms of functional pentagon equation (FPE), known from the theory of integrable models, as an algebraic explanation to the phenomenon known in physics as s<->t duality. We…
I. G. Korepanov, S. SaitoDec 16, 1998
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A Realization of Discrete Geometry by String Model
A realization of discrete conjugate net is presented by using correlation functions of strings in a gauge covariant form.
Satoru SaitoDec 15, 1998
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Inhomogeneous Burgers Equation and the Feynman-Kac Path Integral
By linearizing the inhomogeneous Burgers equation through the Hopf-Cole transformation, we formulate the solution of the initial value problem of the corresponding linear heat type equation using the…
Hans J. Wospakrik, Freddy P. ZenDec 15, 1998
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Solutions to the Optical Cascading Equations
Group theoretical methods are used to study the equations describing χ(2):χ(2) cascading. The equations are shown not to be integrable by inverse scattering techniques. On the other hand, these…
S. Lafortune, P. Winternitz, C. R. MenyukDec 11, 1998
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Optical Fiber Communications:Group of the Nonlinear Transformations
A new method for finding solutions of the nonlinear Shrödinger equation is proposed. Comutative multiplicative group of the nonlinear transformations, which operate on stationary localized solutions,…
S. Lekic, S. Galamic, Z. RajilicDec 11, 1998
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On Discrete Painleve Equations Associated with the Lattice KdV Systems and the Painleve VI Equation
A new integrable nonautonomous nonlinear ordinary difference equation is presented which can be considered to be a discrete analogue of the Painleve V equation. Its derivation is based on the…
F. W. Nijhoff, A. Ramani, B. Grammaticos et al.Dec 10, 1998
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Coverings and integrability of the Gauss-Mainardi-Codazzi equations
Using covering theory approach (zero-curvature representations with the gauge group SL2), we insert the spectral parameter into the Gauss-Mainardi-Codazzi equations in Tchebycheff and geodesic…
Joseph Krasil'shchik, Michal MarvanDec 9, 1998
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The symplectic structure of rational Lax pair systems
We consider dynamical systems associated to Lax pairs depending rationnally on a spectral parameter. We show that we can express the symplectic form in terms of algebro--geometric data provided that…
O. Babelon, M. TalonDec 7, 1998
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Various truncations in Painlevé analysis of PDEs
The ``truncation procedure'' initiated by Weiss et al. is best understood as a Darboux transformation. If it leads to the Lax pair of the PDE under study, the Bäcklund transformation follows…
R. ConteDec 4, 1998
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Perturbative methods for the Painlevé test
There exist many situations where an ordinary differential equation admits a movable critical singularity which the test of Kowalevski and Gambier fails to detect. Some possible reasons are:…
R. ConteDec 4, 1998
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Random matrices, Virasoro algebras, and noncommutative KP
What is the connection of random matrices with integrable systems? Is this connection really useful? The answer to these questions leads to a new and unifying approach to the theory of random…
M. Adler, T. Shiota, P. van MoerbekeDec 3, 1998
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On the Calogero model with negative harmonic term
The Calogero model with negative harmonic term is shown to be equivalent to the set of negative harmonic oscillators. Two time-independent canonical transformations relating both models are…
C. Gonera, M. Majewski, P. MaślankaDec 3, 1998
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On Calogero wave functions
Two properties of Calogero wave functions for rational Calogero models are studied: (i) the representation of the wave functions in terms of the exponential of Lassalle operators, (ii) the…
C. Gonera, P. Kosiński, M. Majewski et al.Dec 3, 1998
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The Coupled Modified Korteweg-de Vries Equations
Generalization of the modified KdV equation to a multi-component system, that is expressed by $(∂ ui)/(∂ t) + 6 (Σj,k=0M-1 Cjk uj uk) (∂ ui)/(∂ x) +…
T. Tsuchida, M. WadatiDec 3, 1998
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Integrable boundary conditions for nonlinear lattices
Integrable boundary conditions in 1+1 and 2+1 dimensions are discussed from the higher symmetries point of view. Boundary conditions consistent with the discrete Landau-Lifshitz model and infinite 2D…
I. T. Habibullin, A. N. Vil'danovDec 3, 1998
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Duality between integrable Stackel systems
For the Stackel family of the integrable systems a non-canonical transformation of the time variable is considered. This transformation may be associated to the ambiguity of the Abel map on the…
Andrey TsiganovNov 27, 1998
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The supersymmetric Camassa-Holm equation and geodesic flow on the superconformal group
We study a family of fermionic extensions of the Camassa-Holm equation. Within this family we identify three interesting classes: (a) equations, which are inherently hamiltonian, describing geodesic…
Chandrashekar Devchand, Jeremy SchiffNov 22, 1998
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