How many types of soliton solutions do we know?

We consider several ways of how one could classify the various types of soliton solutions related to nonlinear evolution equations which are solvable by the inverse scattering method. In doing so we make use of the fundamental analytic solutions, thedressing procedure, the reduction technique and other tools characteristic for that method.

Superintegrability in the Manev Problem and its Real Form Dynamics

We report here the existence of Ermanno-Bernoulli type invariants for the Manev model dynamics which may be viewed upon as remnants of Laplace-Runge-Lenz vector whose conservation is characteristic of the Kepler model. If the orbits are bounded theseinvariants exist only when a certain rationality condition is met and thus we have superintegrability only on a subset of initial values. We analyze real form dynamics of the Manev model and derive that it is always superintegrable. We also discuss the symmetry algebras of the Manev model and its real Hamiltonian form.