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Exactly Solvable and Integrable Systems papers — page 28

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Algebraic properties of the 1+1 dimensional Heisenberg spin field model
The Estabrook-Wahlquist prolongation method is applied to the (compact and noncompact) continuous isotropic Heisenberg model in 1 + 1 dimensions. Using a special realization (an algebra of the…
E. Alfinito, M. Leo, R. A. Leo et al.Apr 17, 1996
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Farey Tree and the Frenkel-Kontorova Model
We solved the Frenkel-Kontorova model with the potential V(u)= -12 |λ|(u- Int[u]-12)2 exactly. For given |λ|, there exists a positive integer qc such that for almost…
Hsien-chung Kao, Shih-Chang Lee, Wen-Jer TzengApr 16, 1996
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Analytic Structure of the Landau-Ginzburg Equation in 2+1 Dimensions
In this paper, two methods are employed to investigate for which values of the parameters, if any, the two-dimensional real Landau-Ginzburg equation possesses the Painleve property. For an ordinary…
Daniel StubbsApr 14, 1996
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Non-perturbative non-integrability of non-homogeneous nonlinear lattices induced by non-resonance hypothesis
We prove the non-integrability (non-existence of additional analytic conserved quantities other than Hamiltonian) for Fermi-Pasta-Ulam (FPU) lattices by virtue of Lyapunov-Kovalevskaya-…
Ken UmenoApr 2, 1996
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Elliptic Ruijsenaars-Schneider and Calogero-Moser hierarchies are governed by the same r-matrix
We demonstrate that in a certain gauge the elliptic Ruijsenaars--Schneider models admit Lax representation governed by the same dynamical r--matrix as their non--relativistic counterparts…
Yuri B. SurisApr 1, 1996
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Approximate Controlability by Control Constraints for Infinite Dimensional Systems
For linear infinite systems the approximate controllability problem by control constraints is considered. Controllability conditions represented via system parameters are obtained. Partial…
B. ShklyarApr 1, 1996
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SO(4) invariant basis functions for strongly correlated Fermi systems
We show how to construct SO(4) invariant functions for strongly correlated Fermi systems on lattices of finite sizes. We illustrate the method on the case of the 1D Hubbard chain with four and with…
Mario SalernoMar 27, 1996
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Ferromagnetic ground states of the Hubbard model on a complete graph
We use group theory to derive the exact analytical expression of the ferromagnetic ground states of the Hubbard model on a complete graph for arbitrary lattice sites f and for arbitrary fillings N.…
Mario SalernoMar 27, 1996
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The Hubbard model on a complete graph: Exact Analytical results
We derive the analytical expression of the ground state of the Hubbard model with unconstrained hopping at half filling and for arbitrary lattice sites.
Mario SalernoMar 27, 1996
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Dynamical r-matrix for the elliptic Ruijsenaars-Schneider system
The classical r-matrix structure for the generic elliptic Ruijsenaars-Schneider model is presented. It makes the integrability of this model as well as of its discrete-time version that was…
F. W. Nijhoff, V. B. Kuznetsov, E. K. Sklyanin et al.Mar 21, 1996
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Hyperelliptic Kleinian functions and applications
We develop the theory of hyperelliptic Kleinian functions. As applications we consider construction of the explicit matrix realization of the hyperelliptic Kummer varieties, differential operators to…
Victor Buchstaber, Victor Enolskii, Dmitri LeykinMar 16, 1996
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Lax representation for two--particle dynamics splitting on two tori
Lax representation in terms of 2× 2 matrices is constructed for a separable multiply--periodic system splitting on two tori. Hyperelliptic Kleinian functions and their reduction to elliptic…
Victor Enolskii, Mario SalernoMar 12, 1996
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Cellular Automata and Ultra-Discrete Painlevé Equations
Starting from integrable cellular automata we present a novel form of Painlevé equations. These equations are discrete in both the independent variable and the dependent one. We show that they…
B. Grammaticos, Y. Ohta, A. Ramani et al.Mar 8, 1996
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From Discrete to Continuous Painlevé Equations: A Bilinear Approach
We present the bilinear forms of the (continuous) Painlevé equations obtained from the continuous limit of the analogous expresssions for the discrete ones. The advantage of this method is that it…
Y. Ohta, A. Ramani, B. Grammaticos et al.Mar 8, 1996
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Darboux Coordinates on Coadjoint Orbits of Lie Algebras
The method of constructing spectral Darboux coordinates on finite dimensional coadjoint orbits in duals of loop algebras is applied to the one pole case, where the orbit is identified with a…
M. R. Adams, J. Harnad, J. HurtubiseMar 5, 1996
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Exact Solution of an Octagonal Random Tiling Model
We consider the two-dimensional random tiling model introduced by Cockayne, i.e. the ensemble of all possible coverings of the plane without gaps or overlaps with squares and various hexagons. At the…
Jan de Gier, Bernard NienhuisFeb 23, 1996
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Some Classes of Solutions to the Toda Lattice Hierarchy
We apply an analogue of the Zakharov-Shabat dressing method to obtain infinite matrix solutions to the Toda lattice hierarchy. Using an operator transformation we convert some of these into solutions…
Harold WidomFeb 8, 1996
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Localized Induction Hierarchy and Weingarten Systems
We describe a method of constructing Weingarten systems of triply orthogonal coordinates, related to the localized induction equation hierarchy of integrable geometric evolution equations
Ron PerlineFeb 1, 1996
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Nonlinear Discrete Systems with Nonanalytic Dispersion Relations
A discrete system of coupled waves (with nonanalytic dispersion relation) is derived in the context of the spectral transform theory for the Ablowitz Ladik spectral problem (discrete version of the…
M. Boiti, J. Leon, F. PempinelliJan 31, 1996
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Bäcklund transformation for the Krichever-Novikov equation
The Bäcklund transformation and its nonlinear superposition principle are presented for the Krichever-Novikov equation ut= uxxx - 3/(2ux) (u2xx - r(u)) + cux, r(5)=0.
V. E. AdlerJan 28, 1996
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Bilinear structure and Schlesinger transforms of the q-P III and q-P VI equations
We show that the recently derived (q-) discrete form of the Painlevé VI equation can be related to the discrete P III, in particular if one uses the full freedom in the implementation of…
M. Jimbo, H. Sakai, A. Ramani et al.Jan 27, 1996
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The Bi-Hamiltonian Structure of the Perturbation Equations of KdV Hierarchy
The bi-Hamiltonian structure is established for the perturbation equations of KdV hierarchy and thus the perturbation equations themselves provide also examples among typical soliton equations.…
Wen-Xiu Ma, Benno FuchssteinerJan 26, 1996
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The Three-Wave Resonant Interaction: Deformation of the Plane-Wave Solutions and Darboux Transformations
The plane wave solutions of the three-wave resonant interaction in the plane are considered. It is shown that rank-one constraints over the right derivatives of invertible operators on an arbitrary…
F. Guil, M. MañasJan 11, 1996
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Hamiltonian Structures for the Generalized Dispersionless KdV Hierarchy
We study from a Hamiltonian point of view the generalized dispersionless KdV hierarchy of equations. From the so called dispersionless Lax representation of these equations we obtain three compatible…
J. C. BrunelliJan 5, 1996
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Constrained KP Hierarchies: Darboux-Bäcklund Solutions and Additional Symmetries
We illustrate the basic notions of additional non-isospectral symmetries and their interplay with the discrete transformations of integrable systems at the instance of …
H. Aratyn, E. Nissimov, S. PachevaDec 28, 1995
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