Avia-Technological Institute, Moscow, RUSSIA

e-mail: maxim.pavlov@mtu.ru

Multi-Lagrangians representations for Integrable Systems, local and nonlocal Hamiltonian structures

Abstract:
We prove and demonstrate that every integrable system possesses at least the same number of local Lagrangian representations as well as number of local Hamiltonian structures. Moreover we show local Lagrangians for some nonlocal Hamiltonian structures. Examples: gas dynamics, KdV, nonlinear Shroedinger equation, Boussinesq & etc... Moreover, we show that gas dynamics allows INFINITE set of local Hamiltonian structures and correspondinly infinite set of Lagrangians written via physical variables (not through their potentials!).