We consider a generalization of the Camassa Holm (CH) equation with two dependent variables, called CH2, introduced in [16]. We briefly provide an alternative derivation of it based on the theory of Hamiltonian structures on ...

We develop the theory of generalized bi-Hamiltonian reduction. Applying this theory to the loop algebra proved to be equivalent to a generalized Drinfeld-Sokolov reduction. This gives a way to construct new examples of ...

We study the critical behaviour of solutions to weakly dispersive Hamiltonian systems considered as perturbations of elliptic and hyperbolic systems of hydrodynamic type with two components. We argue that near the critical ...

For a continuous function f, the set Vf made of those points where the lower left derivative is strictly less than the upper right derivative is totally disconnected. Besides continuity, alternative assumptions are ...

In a measure space (X;A; μ) we consider two measurable functions ƒ; g : E → R for some E ∈ A. We characterize the property of having equal p-norms when ρ varies in an infinite set P in [1;+∞). In a first theorem we consider ...

Hamiltonian perturbations of the simplest hyperbolic equation $u_t + a(u) u_x=0$ are studied. We argue that the behaviour of solutions to the perturbed equation near the point of gradient catastrophe of the unperturbed one ...

Motivated by the study of branes in curved backgrounds, we investigate the construction of non-perturbative extensions of the super-isometry algebra osp*(8|4) of the AdS_7xS^4 background of M-theory. This algebra is not a ...

We prove the absence of positive real resonances for Schrodinger operators with finitely ¨ many point interactions in R 3 and we discuss such a property from the perspective of dispersive and scattering features of the ...

By means of a recently introduced bihamiltonian structure for the homogeneous Gaudin models, we find a new set of Separation Coordinates for the sl(r) case.