In this paper, we derive three conservation laws and three invariants of motion for the generalized Gardner equation. These conserved quantities for internal waves are the momentum, energy, and Hamiltonian. The approach used for the derivation of these conservation laws and their associated...

Invariants of motion are constructed departing from the Gibbs entropy. The method we applied also allows us to find the subspace of a real vector space to which the system is confined to during its temporal evolution. We also find that the Uncertainty Principle is itself an invariant of motion...

We demonstrate that when the Gibbs entropy is an invariant of motion, following Information Theory procedures it is possible to define a generalized metric phase space for the temporal evolution of the mean values of a given Hamiltonian. The metric is positive definite and this fact leads to a...

Using the generalized Ehrenfest theorem the dynamics of the mean values of a complete set of non-commuting observables (CSNCO) associated to a given Hamiltonian is expressed. We found refined time-dependent invariants of motion (TDIM) for the CSNCO, and associated them with different Lie...

Background: The Clustered Orienteering Problem is an optimization problem faced in last-mile logistics. The aim is, given an available time window, to visit vertices and to collect as much profit as possible in the given time. The vertices to visit have to be selected among a set of service...

Lie groups involving potential symmetries are exposed in view of applications to physics. The system of magnetohydrodynamic equations for incompressible matter with Ohm's law for finite resistivity and Hall current is studied in Cartesian geometry. The equations for the evolution of the plasma...