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. In such a framework we introduce the notion of -manifold with compatible connection generalizing a structure introduced by Manin.
O’Grady showed that certain special sextics in called EPW sextics admit smooth double covers with a holomorphic symplectic structure. We propose another perspective on these symplectic manifolds, by showing that they can be constructed from the Hilbert schemes of conics on Fano fourfolds of degree ten. As applications, we construct families of Lagrangian surfaces in these symplectic fourfolds, and related integrable systems whose fibers are intermediate Jacobians.
In this article we prove that the fibration of by potentials which are isospectral for the 1-dimensional periodic Schrödinger equation, is trivial. This result can be applied, in particular, to -gap solutions of the Korteweg-de Vries equation (KdV) on the circle: one shows that KdV, a completely integrable Hamiltonian system, has global action-angle variables.
The paper is devoted to the electromagnetic inverse scattering problem for a dielectric anisotropic and magnetically isotropic media. The properties of an anisotropic medium with respect to electromagnetic waves are defined by the tensors, which give the relation between the inductions and the fields. The tensor Fourier diffraction theorem derived in the paper can be considered a useful tool for studying tensor fields in inverse problems of electromagnetic scattering. The method is based on the...