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We study a symplectic-Haantjes manifold and a Poisson-Haantjes manifold for the Lagrange top and compute a set of Darboux-Haantjes coordinates. Such coordinates are separation variables for the associated Hamilton-Jacobi equation. [ABSTRACT FROM AUTHOR]

Headache is one of the most common neurological diseases. It is well known that there are differences in the perception and in the management of pain in various populations. Immigrants represent a growing portion between neurology outpatients. We analyzed the epidemiological characteristic of headache in immigrants come to our attention, in comparison with Italians. Data collected included age at immigration, age of onset of headache, headache's type (HIS criteria), and psychiatric comorbidities. There were not substantial differences in the incidence of headache subtypes: migraine was the most frequent diagnosis in both groups, followed by tension-type headache. The incidence of depression was similar, while anxiety was significantly less frequent in immigrants. Studies on neurological diseases in immigrants are few. The data available seem to show no differences in the incidence, but rather in treatment. Our study confirms the evenness of two populations, local and foreign, afferent in a Headache Unit, according to the single similar study, except for anxiety, maybe related to language difficulties or cultural background. [ABSTRACT FROM AUTHOR]

Starting from the tri-Hamiltonian formulation of the Lagrange top in a six-dimensional phase space, we discuss the reduction of the vector field and of the Poisson tensors. We show explicitly that after the reduction to each symplectic leaf, the vector field of the Lagrange top is separable in the Hamilton–Jacobi sense. [ABSTRACT FROM AUTHOR]

We discuss the Boussinesq system with the stationary time t5 within a general framework of stationary flows of n-Gel'fand-Dickey hierarchies. A careful use of the bi-Hamiltonian structure can provide a set of separation coordinates for the corresponding Hamilton-Jacobi equations. [ABSTRACT FROM AUTHOR]

A non-abelian prolongation algebra for the three-wave resonant equations in one time and two spatial dimensions is derived. A SL quotient algebra is used to find the linear eigenvalue problem associated with the equations under consideration. [ABSTRACT FROM AUTHOR]

A remarkable map between the generalized Henon-Heiles system and the Garnier system is obtained by means of a detailed comparison between two finite-dimensional reduction methods for soliton equations: the stationary flows and the restricted flows. The role of the Gelfand-Dickey polynomials and of the KdV Poisson pencil in this construction is emphasized. [ABSTRACT FROM AUTHOR]

In the framework of the GN manifold approach, the algebraic structures of two representations of the ILW hierarchy are investigated. It is shown that this hierarchy can be obtained by different realizations of two abstract structures, strictly related with the Yang-Baxter equations. A new reduction theorem for the second representation of ILW is also formulated. [ABSTRACT FROM AUTHOR]

We suggest a method to extend the theory of recursion operators to integrable Hamiltonian systems in two-space dimensions, like KP systems. The approach aims to stress the conceptual unity of the theories in one and two space dimensions. A sound explanation of the appearance of bilocal operators is also given. [ABSTRACT FROM AUTHOR]