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Exactly Solvable and Integrable Systems papers — page 21

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Nonlinear Quasiclassics and the Painlevé Equations
Problem of asymptotic description for global solutions to the six Painleve equations was investigated. Elliptic anzatzes and appropriate modulation equations were written out.
V. L. VereschaginJul 7, 1997
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Statistical Mechanics of Elastica on Plane as a Model of Supercoiled DNA-Origin of the MKdV hierarchy-
In this article, I have investigated statistical mechanics of a non-stretched elastica in two dimensional space using path integral method. In the calculation, the MKdV hierarchy naturally appeared…
Shigeki MatsutaniJul 4, 1997
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Trace Formula for a System of Particles with Elliptic Potential
We consider classical particles on the line with the Weierstrass function as potential. This system parameterizes special solutions of the KP equation. We derive the trace formula which relates…
K. L. VaninskyJul 1, 1997
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The Distribution of the Largest Eigenvalue in the Gaussian Ensembles
The focus of this survey paper is on the distribution function for the largest eigenvalue in the finite N Gaussian ensembles (GOE,GUE,GSE) in the edge scaling limit of N->infinity. These limiting…
Craig A. Tracy, Harold WidomJun 27, 1997
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Matrix Integrals, Toda symmetries, Virasoro constraints, and orthogonal polynomials
The relationship is made between matrix integrals, Toda master-symmetries, Virasoro constraints and orthogonal polynomials.
Mark Adler, Pierre van MoerbekeJun 25, 1997
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The spectrum of random matrices and integrable systems
What is the connection of random matrices with integrable systems? Is this connection really useful? Introducing apprpriate times in the distribution of the ensemble of matrices, one shows that the…
Pierre van MoerbekeJun 25, 1997
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An Extension of the KdV Hierarchy Arising from a Representation of a Toroidal Lie Algebra
In this article we show how to construct hierarchies of partial differential equations from the vertex operator representations of toroidal Lie algebras. In the smallest example - rank 2 toroidal…
Yuly BilligJun 18, 1997
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On the Liouville transformation and exactly-solvable Schrodinger equations
The present article discusses the connection between exactly-solvable Schrodinger equations and the Liouville transformation. This transformation yields a large class of exactly-solvable potentials,…
Robert MilsonJun 15, 1997
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The geometry of spinors and the multicomponent BKP and DKP hierarchies
We develop a formalism of multicomponent BKP hierarchies using elementary geometry of spinors. The multicomponent KP and the modified KP hierarchy (hence all their reductions like KdV, NLS, AKNS or…
Victor Kac, Johan van de LeurJun 6, 1997
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A Lax Description for Polytropic Gas Dynamics
We give a Lax description for the system of polytropic gas equations. The special structure of the Lax function naturally leads to the two infinite sets of conserved charges associated with this…
J. C. Brunelli, A. DasJun 5, 1997
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An analytic description of the vector constrained KP hierarchy
In this paper we give a geometric description in terms of the Grassmann manifold of Segal and Wilson, of the reduction of the KP hierarchy known as the vector k-constrained KP hierarchy. We also…
G. F. Helminck, J. W. van de LeurJun 5, 1997
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On the point transformations for the equation y''= P + 3Qy' + 3Ry'2 + Sy'3
For the equations y''=P(x,y) + 3Q(x,y)y' + 3R(x,y)y'2 + S(x,y)y'3 the problem of equivalence is considered. Some classical results are resumed in order to prepare the…
R. A. SharipovJun 5, 1997
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Integrable Fredholm Operators and Dual Isomonodromic Deformations
The Fredholm determinants of a special class of integral operators K supported on the union of m curve segments in the complex plane are shown to be the tau-functions of an isomonodromic family of…
J. Harnad, Alexander R. ItsJun 5, 1997
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R-Matrices and Generalized Inverses
Four results are given that address the existence, ambiguities and construction of a classical R-matrix given a Lax pair. They enable the uniform construction of R-matrices in terms of any…
H. W. BradenMay 30, 1997
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Algebro-Geometric Quasi-Periodic Finite-Gap Solutions of the Toda and Kac-van Moerbeke Hierarchies
Combining algebro-geometric methods and factorization techniques for finite difference expressions we provide a complete and self-contained treatment of all real-valued quasi-periodic finite-gap…
W. Bulla, F. Gesztesy, H. Holden et al.May 29, 1997
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Dual Isomonodromic Problems and Whitham Equations
The author's recent results on an asymptotic description of the Schlesinger equation are generalized to the JMMS equation. As in the case of the Schlesinger equation, the JMMS equation is…
Kanehisa TakasakiMay 28, 1997
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A Characterization of All Elliptic Solutions of the AKNS Hierarchy
An explicit characterization of all elliptic algebro-geometric solutions of the AKNS hierarchy is presented. Our approach is based on (an extension of) a classical theorem of Picard, which guarantees…
Fritz Gesztesy, Rudi WeikardMay 28, 1997
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Laplace transformations of hydrodynamic type systems in Riemann invariants: periodic sequences
The conserved densities of hydrodynamic type system in Riemann invariants satisfy a system of linear second order partial differential equations. For linear systems of this type Darboux introduced…
E. V. FerapontovMay 28, 1997
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Graded Symmetry Algebras of Time-Dependent Evolution Equations and Application to the Modified KP equations
By starting from known graded Lie algebras, including Virasoro algebras, new kinds of time-dependent evolution equations are found possessing graded symmetry algebras. The modified KP equations are…
W. X. Ma, R. K. Bullough, P. J. CaudreyMay 27, 1997
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Time-Dependent Symmetries of Variable-Coefficient Evolution Equations and Graded Lie Algebras
Polynomial-in-time dependent symmetries are analysed for polynomial-in-time dependent evolution equations. Graded Lie algebras, especially Virasoro algebras, are used to construct nonlinear…
W. X. Ma, R. K. Bullough, P. J. Caudrey et al.May 27, 1997
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Dispersionless Hierarchies, Hamilton-Jacobi Theory and Twistor Correspondences
The dispersionless KP and Toda hierarchies possess an underlying twistorial structure. A twistorial approach is partly implemented by the method of Riemann-Hilbert problem. This is however still…
Partha Guha, Kanehisa TakasakiMay 22, 1997
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Vectorial Darboux Transformations for the Kadomtsev-Petviashvili Hierarchy
We consider the vectorial approach to the binary Darboux transformations for the Kadomtsev-Petviashvili hierarchy in its Zakharov-Shabat formulation. We obtain explicit formulae for the Darboux…
Q. P. Liu, M. ManasMay 21, 1997
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Stationary mKdV hierarchy and integrability of the Dirac equations by quadratures
Using the Lie's infinitesimal method we establish that the Dirac equation in one variable is integrable by quadratures if the potential V(x) is a solution of one of the equations of the…
Renat Zhdanov, Ihor Revenko, Wilhelm FushchychMay 17, 1997
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Integrability of Riccati equations and the stationary KdV equations
Using the S.Lie's infinitesimal approach we establish the connection between integrability of a one-parameter family of the Riccati equations and the stationary KdV hierarchy.
Renat ZhdanovMay 17, 1997
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Analytic-bilinear approach to integrable hierarchies. II. Multicomponent KP and 2D Toda lattice hierarchies
Analytic-bilinear approach for construction and study of integrable hierarchies is discussed. Generalized multicomponent KP and 2D Toda lattice hierarchies are considered. This approach allows to…
L. V. Bogdanov, B. G. KonopelchenkoMay 16, 1997
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