Abelian varieties, surfaces of general type and integrable systems.
An explicit separate solution for the Tzitzeica equation.
Bifurcation analysis for a delayed predator-prey system with stage structure.
Commutative rings of differential operators corresponding to multidimensional algebraic varieties.
Desingularization of a Hyperelliptic Curve Associated with a Doubly Periodic Dirac Potential
Dimensions of Prym varieties.
Endomorphisms of symbolic algebraic varieties
The theorem of Ax says that any regular selfmapping of a complex algebraic variety is either surjective or non-injective; this property is called surjunctivity and investigated in the present paper in the category of proregular mappings of proalgebraic spaces. We show that such maps are surjunctive if they commute with sufficiently large automorphism groups. Of particular interest is the case of proalgebraic varieties over infinite graphs. The paper intends to bring out relations between model theory,...
Fano manifolds of degree ten and EPW sextics
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.
Further extended sinh-cosh and sin-cos methods and new nontraveling wave solutions of the -dimensional dispersive long wave equations.
Hamiltonian structure of pi hierarchy.
Integrability and beyond
Loop groups and equations of KdV type
Majorations affines du nombre de zéros d'intégrales abéliennes pour les hamiltoniens quartiques elliptiques
Modulation of the Camassa-Holm equation and reciprocal transformations
We derive the modulation equations (Whitham equations) for the Camassa-Holm (CH) equation. We show that the modulation equations are hyperbolic and admit a bi-Hamiltonian structure. Furthermore they are connected by a reciprocal transformation to the modulation equations of the first negative flow of the Korteweg de Vries (KdV) equation. The reciprocal transformation is generated by the Casimir of the second Poisson bracket of the KdV averaged flow. We show that the geometry...
Monopoles and modifications of bundles over elliptic curves.
Multi-component NLS models on symmetric spaces: spectral properties versus representations theory.
On commuting differential operators.
On nonlinear equations integrable in theta-functions of nonprincipally polarized Abelian varieties.
On quadrirational Yang-Baxter maps.
On rational and periodic solutions of stationary KdV equations.