Generalized Poisson brackets and nonlinear Liapunov stability-application to reduced MHD

Hazeltine, R. D., D. D. Holm, J. E. Marsden and P. J. Morrison

In ICCP Proc., (Lausanne), 2, (1984), 204-206


A method is presented for obtaining Liapunov functionals (LF) and proving nonlinear stability. The method uses the generalized Poisson bracket (GPB) formulation of Hamiltonian dynamics. As an illustration, certain stationary solutions of ideal reduced MHD (RMHD) are shown to be nonlinearly stable. This includes Grad-Shafranov and Alfven solutions.