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Exactly Solvable and Integrable Systems papers — page 14

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On The Stability of the Compacton Solutions
The stability of the recently discovered compacton solutions is studied by means of both linear stability analysis as well as Lyapunov stability criteria. From the results obtained it follows that,…
Bishwajyoti Dey, Avinash KhareApr 25, 1998
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Travelling Wave Solutions in Nonlinear Diffusive and Dispersive Media
We investigate the presence of soliton solutions in some classes of nonlinear partial differential equations, namely generalized Korteweg-de Vries-Burgers, Korteveg-de Vries-Huxley, and Korteveg-de…
D. Bazeia, E. P. RaposoApr 25, 1998
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Elliptic solutions to difference non-linear equations and nested Bethe ansatz equations
We outline an approach to a theory of various generalizations of the elliptic Calogero-Moser (CM) and Ruijsenaars-Shneider (RS) systems based on a special inverse problem for linear operators with…
I. M. KricheverApr 15, 1998
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Knizhnik-Zamolodchikov-Bernard equations connected with the eight-vertex model
Using quasiclassical limit of Baxter's 8 - vertex R - matrix, an elliptic generalization of the Knizhnik-Zamolodchikov equation is constructed. Via Off-Shell Bethe ansatz an integrable…
H. Babujian, A. Lima-Santos, R. H. PoghossianApr 15, 1998
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The Gel'fand-Tsetlin Selection Rules and Representations of Quantum Algebras
The problem of construction of irreducible representations of quantum Aqn algebras is solved at the level of explicit integration of the linear (inhomogeneous) system in finite differences in the…
A. N. LeznovApr 13, 1998
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Higher Order Asymptotics of the Modified Non-Linear Schrödinger Equation
Using the matrix Riemann-Hilbert factorisation approach for non-linear evolution systems which take the form of Lax-pair isospectral deformations, the higher order asymptotics as t ∞…
A. H. VartanianApr 12, 1998
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Again, Linearizable Mappings
We examine a family of 3-point mappings that include mappings solvable through linearization. The different origins of mappings of this type are examined: projective equations and Gambier systems.…
A. Ramani, B. Grammaticos, S. LafortuneApr 10, 1998
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The Gambier Mapping, Revisited
We examine critically the Gambier equation and show that it is the generic linearisable equation containing, as reductions, all the second-order equations which are integrable through linearisation.…
B. Grammaticos, A. Ramani, S. LafortuneApr 10, 1998
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Determinant formula for the six-vertex model with reflecting end
Using the Quantum Inverse Scattering Method for the XXZ model with open boundary conditions, we obtained the determinant formula for the six vertex model with reflecting end.
O. TsuchiyaApr 10, 1998
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The Davey Stewartson system and the Bäcklund Transformations
We consider the (coupled) Davey-Stewartson (DS) system and its Bäcklund transformations (BT). Relations among the DS system, the double Kadomtsev-Petviashvili (KP) system and the Ablowitz-Ladik…
Masato HisakadoApr 9, 1998
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Modular Solutions to Equations of Generalized Halphen Type
Solutions to a class of differential systems that generalize the Halphen system are determined in terms of automorphic functions whose groups are commensurable with the modular group. These functions…
J. Harnad, J. McKayApr 9, 1998
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On the exact solutions of the Bianchi IX cosmological model in the proper time
It has recently been argued that there might exist a four-parameter analytic solution to the Bianchi IX cosmological model, which would extend the three-parameter solution of Belinskii et al. to one…
J. Springael, R. Conte, M. MusetteApr 8, 1998
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Novel integrable spin-particle models from gauge theories on a cylinder
We find and solve a large class of integrable dynamical systems which includes Calogero-Sutherland models and various novel generalizations thereof. In general they describe N interacting particles…
Jonas Blom, Edwin LangmannApr 8, 1998
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On the relation between orthogonal, symplectic and unitary matrix ensembles
For the unitary ensembles of N× N Hermitian matrices associated with a weight function w there is a kernel, expressible in terms of the polynomials orthogonal with respect to the weight…
Harold WidomApr 3, 1998
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Correlation Functions, Cluster Functions and Spacing Distributions for Random Matrices
The usual formulas for the correlation functions in orthogonal and symplectic matrix models express them as quaternion determinants. From this representation one can deduce formulas for spacing…
Craig A. Tracy, Harold WidomApr 2, 1998
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Painlevé analysis for nonlinear partial differential equations
The Painlevé analysis introduced by Weiss, Tabor and Carnevale (WTC) in 1983 for nonlinear partial differential equations (PDE's) is an extension of the method initiated by Painlevé and Gambier…
M. MusetteMar 31, 1998
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The system of three vortexes of two dimensional ideal hydrodinamics as a new example of the (integrable) Nambu- Poisson mechanics
A Nambu-Poisson formulation of the system of three ordinary differential equations describing dynamics of three vortexes of the ideal two-dimensional hydrodynamics is given. The system is integrated…
N. MakhaldianiMar 31, 1998
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On lump instability of Davey--Stewartson II equation
We show that lumps (solitons) of the Davey--Stewartson II equation fail under small perturbations of initial data.
R. R. Gadyl'shin, O. M. KiselevMar 31, 1998
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Asymptotics of perturbed soliton for Davey--Stewartson II equation
It is shown that, under a small perturbation of lump (soliton) for Davey--Stewartson (DS-II) equation, the scattering data gain the nonsoliton structure. As a result, the solution has the form of…
R. R. Gadyl'shin, O. M. KiselevMar 31, 1998
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All generalized SU(2) chiral models have spectral dependent Lax formulation
The equations that define the Lax pairs for generalized principal chiral models can be solved for any nondegenerate bilinear form on su(2). The solution is dependent on one free variable that can…
L. HlavatyMar 26, 1998
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Integrable discretizations of the Euler top
Discretizations of the Euler top sharing the integrals of motion with the continuous time system are studied. Those of them which are also Poisson with respect to the invariant Poisson bracket of the…
A. I. Bobenko, B. Lorbeer, Yu. B. SurisMar 23, 1998
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Charged Free Fermions, Vertex Operators and Classical Theory of Conjugate Nets
We show that the quantum field theoretical formulation of the τ-function theory has a geometrical interpretation within the classical transformation theory of conjugate nets. In particular, we…
Adam Doliwa, Manuel Manas, Luis Martinez Alonso et al.Mar 20, 1998
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Rules of discretization for Painlevé equations
The discrete Painlevé property is precisely defined, and basic discretization rules to preserve it are stated. The discrete Painlevé test is enriched with a new method which perturbs the continuum…
R. Conte, M. MusetteMar 18, 1998
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N-Soliton Solutions to a New (2 + 1) Dimensional Integrable Equation
We give explicitly N-soliton solutions of a new (2 + 1) dimensional equation, ϕxt + ϕxxxz/4 + ϕx ϕxz + ϕxx ϕz/2 + ∂x-1 ϕzzz/4 = 0. This equation is obtained by unifying…
S. J. Yu, K. Toda, T. FukuyamaMar 18, 1998
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On the simplest (2+1) dimensional integrable spin systems and their equivalent nonlinear Schrödinger equations
Using a moving space curve formalism, geometrical as well as gauge equivalence between a (2+1) dimensional spin equation (M-I equation) and the (2+1) dimensional nonlinear Schrödinger equation (NLSE)…
R. Myrzakulov, S. Vijayalakshmi, R. N. Syzdykova et al.Mar 13, 1998
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