A Symplectic Generalization of the Peradzynski Helicity Theorem and Some Applications

Prykarpatsky, Anatoliy K.; Bogoliubov Jr., Nikolai N.; Golenia, Jolanta

A Symplectic Generalization of the Peradzynski Helicity Theorem and Some Applications

Authors

Prykarpatsky, Anatoliy K.

Bogoliubov Jr., Nikolai N.

Golenia, Jolanta

Description

Symplectic and symmetry analysis for studying MHD superfluid flows is devised, a new version of the Z. Peradzynski helicity theorem based on differential - geometric and group-theoretical methods is derived. Having reanalyzed the Peradzynski helicity theorem within the modern symplectic theory of differential- geometric structures on manifolds, a new unified proof and a new generalization of this theorem for the case of compressible MHD superfluid flow are proposed. As a by-product, a sequence of nontrivial helicity type local and global conservation laws for the case of incompressible superfluid flow, playing a crucial role for studying the stability problem under suitable boundary conditions, is constructed.