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Exactly Solvable and Integrable Systems papers — page 27

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Coupled Integrable Systems Associated with a Polynomial Spectral Problem and their Virasoro Symmetry Algebras
An isospectral hierarchy of commutative integrable systems associated with a polynomial spectral problem is proposed. The resulting hierarchy possesses a recursion structure controlled by a…
Wen-Xiu MA, Zi-Xiang ZHOUJul 16, 1996
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Determinant Structure of the Rational Solutions for the Painlevé II Equation
Two types of determinant representations of the rational solutions for the Painlevé II equation are discussed by using the bilinear formalism. One of them is a representation by the Devisme…
Kenji Kajiwara, Yasuhiro OhtaJul 15, 1996
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Exact Solution of Frenkel-Kontorova Models with a Complete Devil's Staircase in Higher Dimensions
We solve exactly a class of Frenkel-Kontorova models with piecewise parabolic potential, which has d sub-wells in a period. With careful analysis, we show that the phase diagram of the minimum…
Hsien-chung Kao, Shih-Chang Lee, Wen-Jer TzengJul 8, 1996
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A Note on Fractional KdV Hierarchies
We introduce a hierarchy of mutually commuting dynamical systems on a finite number of Laurent series. This hierarchy can be seen as a prolongation of the KP hierarchy, or a ``reduction'' in…
Paolo Casati, Gregorio Falqui, Franco Magri et al.Jul 4, 1996
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On a generalization of the Fay-Sato identity for KP Baker functions and its application to constrained hierarchies
Some new formulas for the KP hierarchy are derived from the differential Fay identity. They proved to be useful for the k-constrained hierarchies providing a series of determinant identities for…
L. A. Dickey, W. StramppJul 3, 1996
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Loop algebras, gauge invariants and a new completely integrable system
One fruitful motivating principle of much research on the family of integrable systems known as ``Toda lattices'' has been the heuristic assumption that the periodic Toda lattice in an affine…
M. Quinn, S. F. SingerJun 25, 1996
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Generalized integrable hierarchies and Combescure symmetry transformations
Unifying hierarchies of integrable equations are discussed. They are constructed via generalized Hirota identity. It is shown that the Combescure transformations, known for a long time for the…
L. V. Bogdanov, B. G. KonopelchenkoJun 20, 1996
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On the geometry of certain isospectral sets in the full Kostant-Toda lattice
We use momentum mappings on generalized flag manifolds and their momentum polytopes to study the geometry of the level sets of the 1-chop integrals of the full Kostant-Toda lattice in certain…
Barbara ShipmanJun 19, 1996
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Some survey remarks on Whitham theory and EM duality
The nature of the BA function and its adjoint for KP-Toda is traced through the averaging method in generating the Whitham equations, differentials, and symplectic forms, with connections to EM…
R. CarrollJun 18, 1996
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Symmetries of KdV and Loop Groups
A simple version of the Segal-Wilson map from the SL(2,C) loop group to a class of solutions of the KdV hierarchy is given, clarifying certain aspects of this map. It is explained how the known…
Jeremy SchiffJun 13, 1996
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On completeness of the Ribaucour transformations for triply orthogonal curvilinear coordinate systems in R3
In this paper we solve positively the problem of (local) density of solutions of the (2+1)-dimentional integrable system describing triply orthogonal curvilinear coordinates in R3 (a…
E. I. GanzhaJun 11, 1996
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On completeness of the Moutard transformations
In this paper we solve positively the problem of (local) density of the "potentials" M(x,y) of the Moutard equation, uxy = M(x,y) u, u=u(x,y), (used in many papers for construction of…
E. I. GanzhaJun 11, 1996
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On superposition of the autoBaecklund transformations for (2+1)-dimensional integrable systems
The usual superposition formulas for Baecklund transformations of (2+1)-dimensional integrable systems include quadratures unlike the well known case of (1+1)-dimensional inegrable systems where the…
E. T. Ganzha, S. P. TsarevJun 11, 1996
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A new integrable system related to the Toda lattice
A new integrable lattice system is introduced, and its integrable discretizations are obtained. A Bäcklund transformation between this new system and the Toda lattice, as well as between their…
Yuri B. SurisJun 5, 1996
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Binary Nonlinearization of Lax Pairs
A kind of Bargmann symmetry constraints involving Lax pairs and adjoint Lax pairs is proposed for soliton hierarchy. The Lax pairs and adjoint Lax pairs are nonlinearized into a hierarchy of…
Wen-Xiu Ma, Benno FuchssteinerMay 31, 1996
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On a class of rational and mixed soliton-rational solutions of Toda lattice
A class of rational solutions of Toda lattice satisfying certain Backlund transformations and a class of mixed rational-soliton solutions (quasisolitons) in wronskian formare obtained using the…
A. S. Cârstea, D. GrecuMay 28, 1996
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Higher Order SUSY in Quantum Mechanics and Integrability of Two-dimensional Hamiltonians
The new method based on the SUSY algebra with supercharges of higher order in derivatives is proposed to search for dynamical symmetry operators in 2-dim quantum and classical systems. These symmetry…
A. A. Andrianov, M. V. Ioffe, D. N. NishnianidzeMay 27, 1996
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New integrable systems related to the relativistic Toda lattice
New integrable lattice systems are introduced, their different integrable discretization are obtained. Bäcklund transformations between these new systems and the relativistic Toda lattice (in the…
Yuri B. SurisMay 22, 1996
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A stability analysis for the Korteweg-de Vries equation
In this paper the stability of the Korteweg-de Vries (KdV) equation is investigated. It is shown analytically and numerically that small perturbations of solutions of the KdV-equation introduce…
H. J. S. Dorren, R. K. SniederMay 22, 1996
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Classification of Integrable Evolution Equations of the Form ut=uxxx+f(t,x,u,ux,uxx)
We obtain the classification of integrable equations of the form ut=uxxx+f(t,x,u,ux,uxx) using the formal symmetry method of Mikhailov et al [A.V.Mikhailov, A.B.Shabat and V.V.Sokolov, in…
Ayse Humeyra BilgeMay 17, 1996
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The Painlevé Test of Higher Dimensional KdV Equation
We argue the integrability of the generalized KdV(GKdV) equation using the Painlevé test. For d( 2) dimensional space, GKdV equation passes the Painlevé test but does not for d ≥ 3…
Yu. Song-Ju, T. FukuyamaMay 16, 1996
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Darboux Transformations for a Lax Integrable System in 2n-Dimensions
A 2n-dimensional Lax integrable system is proposed by a set of specific spectral problems. It contains Takasaki equations, the self-dual Yang-Mills equations and its integrable hierarchy as…
Wen-Xiu MaMay 15, 1996
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Integrable discretizations of the spin Ruijsenaars-Schneider models
Integrable discretizations are introduced for the rational and hyperbolic spin Ruijsenaars--Schneider models. These discrete dynamical systems are demonstrated to belong to the same integrable…
O. Ragnisco, Yu. B. SurisMay 3, 1996
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Painlevé Transcendent Describes Quantum Correlation Function of the XXZ Antiferromagnet away from the free-fermion point
We consider quantum correlation functions of the antiferromagnetic spin-12 Heisenberg XXZ spin chain in a magnetic field. We show that for a magnetic field close to the critical field…
Fabian H. L. Essler, Holger Frahm, Alexander R. Its et al.Apr 25, 1996
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Integrable Theory of the Perturbation Equations
An integrable theory is developed for the perturbation equations engendered from small disturbances of solutions. It includes various integrable properties of the perturbation equations: hereditary…
W. X. Ma, B. FuchssteinerApr 22, 1996
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