Algebro-geometric Integration in Classical and Statistical Mechanics
Algebro-geometric solutions of the Camassa-Holm hierarchy.
We provide a detailed treatment of the Camassa-Holm (CH) hierarchy with special emphasis on its algebro-geometric solutions. In analogy to other completely integrable hierarchies of soliton equations such as the KdV or AKNS hierarchies, the CH hierarchy is recursively constructed by means of a basic polynomial formalism invoking a spectral parameter. Moreover, we study Dubrovin-type equations for auxiliary divisors and associated trace formulas, consider the corresponding algebro-geometric initial...
An integrable flow on a family of Hilbert Grassmannians.
Andrew Lenard: a mystery unraveled.
Asymptotics of the partition function of a random matrix model
We prove a number of results concerning the large asymptotics of the free energy of a random matrix model with a polynomial potential. Our approach is based on a deformation of potential and on the use of the underlying integrable structures of the matrix model. The main results include the existence of a full asymptotic expansion in even powers of of the recurrence coefficients of the related orthogonal polynomials for a one-cut regular potential and the double scaling asymptotics of the free...
Auxiliary linear problem, difference Fay identities and dispersionless limit of Pfaff-Toda hierarchy.
Bäcklund transformations for first and second Painlevé hierarchies.
Bidifferential calculus approach to AKNS hierarchies and their solutions.
Bi-integrable and tri-integrable couplings of a soliton hierarchy associated withSO(4)
In our paper, the theory of bi-integrable and tri-integrable couplings is generalized to the discrete case. First, based on the six-dimensional real special orthogonal Lie algebra SO(4), we construct bi-integrable and tri-integrable couplings associated with SO(4) for a hierarchy from the enlarged matrix spectral problems and the enlarged zero curvature equations. Moreover, Hamiltonian structures of the obtained bi-integrable and tri-integrable couplings are constructed by the variational identities....
Bound states in completely integrable systems with two types of particles
By Magri's theorem, self-dual gravity is completely integrable.
-integrability test for discrete equations via multiple scale expansions.
Calogero-Moser spaces and an adelic -algebra
We introduce a Lie algebra, which we call adelic -algebra. Then we construct a natural bosonic representation and show that the points of the Calogero-Moser spaces are in 1:1 correspondence with the tau-functions in this representation.
Chains of KP, semi-infinite 1-Toda lattice hierarchy and Kontsevich integral.
Chapitre VI Compactification d’actions de et variables action-angle avec singularités
Classical -operators and integrable generalizations of Thirring equations.
Clifford algebra derivations of tau-functions for two-dimensional integrable models with positive and negative flows.
Commutative rings of differential operators corresponding to multidimensional algebraic varieties.
Compatible flat metrics.
Completely integrable systems associated with classical root systems.