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We show that the dimer model on a bipartite graph $Γ$ on a torus gives rise to a quantum integrable system of special type, which we call acluster integrable system. The phase space of the classical system contains, as an open dense subset, the moduli space $Ł_{Γ}$ of line bundles with connections on the graph $Γ$ . The sum of Hamiltonians is essentially the partition function of the dimer model. We say that two such graphs $Γ_{1}$ and $Γ_{2}$ areequivalentif the Newton polygons of the corresponding partition functions...

Diophantine conditions in global well-posedness for coupled KdV-type systems.

Oh, Tadahiro (2009)

Electronic Journal of Differential Equations (EJDE) [electronic only]

Discrete isothermic surfaces.

Ulrich Pinkall, Alexander Bobenko (1996)

Journal für die reine und angewandte Mathematik

Dispersionless Hirota equations of two-component BKP hierarchy.

Takasaki, Kanehisa (2006)

SIGMA. Symmetry, Integrability and Geometry: Methods and Applications [electronic only]

Dissipative initial boundary value problem for the BBM-equation.

Larkin, Nikolai A., Vishnevskii, Mikhail P. (2008)

Electronic Journal of Differential Equations (EJDE) [electronic only]

Distribution laws for integrable eigenfunctions

Bernard Shiffman, Tatsuya Tate, Steve Zelditch (2004)

Annales de l’institut Fourier

We determine the asymptotics of the joint eigenfunctions of the torus action on a toric Kähler variety. Such varieties are models of completely integrable systems in complex geometry. We first determine the pointwise asymptotics of the eigenfunctions, which show that they behave like Gaussians centered at the corresponding classical torus. We then show that there is a universal Gaussian scaling limit of the distribution function near its center. We also determine the limit...

Divergences in formal variational calculus and boundary terms in Hamiltonian formalism

Vladimir Soloviev (1997)

Banach Center Publications

It is shown how to extend the formal variational calculus in order to incorporate integrals of divergences into it. Such a generalization permits to study nontrivial boundary problems in field theory on the base of canonical formalism.

Do all integrable evolution equations have the Painlevé property?

Tamizhmani, K.M., Grammaticos, Basil, Ramani, Alfred (2007)

SIGMA. Symmetry, Integrability and Geometry: Methods and Applications [electronic only]

Drift and diffusion in phase space

L. Chierchia, G. Gallavotti (1994)

Annales de l'I.H.P. Physique théorique

Drinfeld-Sokolov hierarchies on truncated current Lie algebras

Paolo Casati (2011)

Banach Center Publications

In this paper we construct on truncated current Lie algebras integrable hierarchies of partial differential equations, which generalize the Drinfeld-Sokolov hierarchies defined on Kac-Moody Lie algebras.

Dubrovin Type Equations for Completely Integrable Systems Associated with a Polynomial Pencil

Yordanov, Russi (1998)

Serdica Mathematical Journal

Dubrovin type equations for the N -gap solution of a completely integrable system associated with a polynomial pencil is constructed and then integrated to a system of functional equations. The approach used to derive those results is a generalization of the familiar process of finding the 1-soliton (1-gap) solution by integrating the ODE obtained from the soliton equation via the substitution u = u(x + λt).

Dynamical systems -- past and present.

Moser, Jürgen (1998)

Documenta Mathematica

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