Terms Of Action Variables Research Articles

Estimates for solutions of KDV on the phase space of periodic distributions in terms of action variables

We consider the KdV equation on the Sobolev space of periodic distributions. We obtain estimates of the solution of the KdV in terms of action variables.

Application of Lie transform perturbation method for multidimensional non-Hermitian systems

Three-dimensional non-Hermitian systems are investigated using classical perturbation theory based on Lie transformations. Analytic expressions for total energy in terms of action variables are derived. Both real and complex semiclassical eigenvalues are obtained by quantizing the action variables. It was found that semiclassical energy eigenvalues calculated with the classical perturbation theory are in very good agreement with exact energies and for certain non-Hermitian systems second-order classical perturbation theory performed better than the second-order Rayleigh–Schroedinger perturbation theory.

Complete Integrability of Nonlinear Network Equations Describing a Volterra System

Nonlinear network equations equivalent to Volterra's competition equations, which was solved by the inverse scattering method in a previous paper, are shown to describe a completely integrable Hamiltonian system. A roundabout is taken to put the equations into the canonical form. Extended equations are proposed, which reduce to the equations for the Volterra system when certain constraints for potentials are satisfied. The generalized system can be analyzed by the standard canonical formulation. The constraints are rewritten first by means of scattering data and then of action-angle variables. The Hamiltonian for the extended system as well as the Volterra system can be expressed only in terms of action variables.