This paper surveys the classification of integrable evolution equations whose field variables
take values in an associative algebra, which includes matrix, Clifford, and group algebra …

Abstract Contents Introduction Chapter I. Differential geometry of symplectic structures on
loop spaces of smooth manifolds § 1.1. Symplectic and Poisson structures on loop spaces of …

Recently, a hydrodynamic description of local equilibrium dynamics in quantum integrable
systems was discovered. In the diffusionless limit, this is equivalent to a certain'Bethe …

EV Ferapontov, “Differential geometry of nonlocal Hamiltonian operators of hydrodynamic type”,
Funktsional. Anal. i Prilozhen., 25:3 (1991), 37–49; Funct. Anal. Appl., 25:3 (1991), 195–204 …

We investigate Hamiltonian aspects of the integro-differential kinetic equation for dense
soliton gas which results as a thermodynamic limit of the Whitham equations. Under a delta …

We connect two a priori unrelated topics, the theory of geodesically equivalent metrics in
differential geometry, and the theory of compatible infinite-dimensional Poisson brackets of …

We exhibit the bi-Hamiltonian structure of the equations of associativity (Witten-Dijkgraaf-
Verlinde-Verlinde-Dubrovin equations) in 2-d topological field theory, which reduce to a …

We investigate the role of Hertling-Manin condition on the structure constants of an
associative commutative algebra in the theory of integrable systems of hydrodynamic type …

We study algebraic and projective geometric properties of Hamiltonian trios determined by a
constant coefficient second-order operator and two first-order localizable operators of …

We consider the quasiclassical limit of the first nontrivial flow in coupled KdV hierarchy.
Written down in Riemann invariants, it assumes the extremely simple form R+ i=∑ k= 1 n R …