[en] The numbered asteroids are classified into families by a new method previously proposed by the author using the semi-major axis, the minimum value of the inclination and the argument of the perihelion as parameters, and the class characteristics are studied by several aspects. It seems to the author that there are two kinds of families, one being very compact in the phase space and containing many faint as well as a few bright asteroids and one being rather loose and bounded by secular and mean motion commensurable regions. (Auth.)

[en] Very simple arguments are used to show that some mathematically attractive viscous stresses, which prevent the formation of shocks and give a parabolic character to the equations of motion for continua in which they appear, are physically unacceptable because their material responses are affected by rigid motion.

[en] We present a geometric proof of Liouville's theorem on the existence of canonical coordinates for integrable systems. (Author)

[en] Published in summary form only

No abstract available

[en] We introduce the Richelot class of superintegrable systems in N-dimensions whose n ≤ N equations of motion coincide with the Abel equations on the n - 1 genus hyperelliptic curve. Corresponding additional integrals of motion are the second-order polynomials of momenta and multiseparability of the Richelot superintegrable systems is related to the classical theory of covers of the hyperelliptic curves.

[en] The book consists of the Proceedings of the School on Qualitative Aspects and Applications of Nonlinear Evolution equations held at the ICTP Trieste between 10 September-5 October 1990. It includes Main Courses (5 lectures), Special Lectures (7 lectures) and Talks Given at the Seminars (13 lectures). A separate abstract was prepared for each lecture. Refs, figs and tabs

[en] The motion of a soliton in a supergravity background configuration is studied. The dynamics of the soliton is desribed by a trajectory in curved N = 2 superspace. For the proposed Langrangian the moments, the constraints and the generators of local supertranslations are displayed. An additional local gauge symmetry is exhibited. Special emphasis is laid on the classical equations of motion. These turn out to be a supersymmetric generalization of Papapetrou's equation of motion for a spinning particle in a gravitational field. (Author)

[en] We derive an exact equation of motion for a non-relativistic vortex in two- and three-dimensional models with a complex field. The velocity is given in terms of gradients of the complex field at the vortex position. We discuss the problem of reducing the field dynamics to a closed dynamical system with non-locally interacting strings as the fundamental degrees of freedom

[en] We consider the generalized Staeckel systems, the broadest class of integrable Hamiltonian systems that admit separation of variables and possess separation relations affine in the Hamiltonians. For these systems we construct in a systematic fashion hierarchies of basic separable potentials. Moreover, we show how the equations of motion for the systems under study are related through appropriately chosen reciprocal transformations and how the respective constants of motion are related through generalized Staeckel transforms. -- Highlights: → We consider the generalized Staeckel systems defined by an appropriate separation relations. → For various classes of these systems we construct hierarchies of basic separable potentials. → We show how the systems from different classes are related through reciprocal transformations. → We show how the respective constants of motion are related through generalized Saeckel transforms.