1) We identify new parameter branches for the ultra-local boundary Poisson bracket in d spatial dimension with a (d− 1)-dimensional spatial boundary. There exist 2 r-dimensional parameter branches for each d-box, r-row Young tableau. The already known branch (hepth/9912017) corresponds to a vertical 1-column, d-box Young tableau. 2) We consider a local distribution product among the so-called b...

The conservation of the Hamiltonian structures in Whitham's method of averaging. Abstract The work is devoted to the proof of the conservation of local field-theoretical Hamiltonian structures in Whitham's method of averaging. The consideration is based on the procedure of averaging of local Pois-son bracket, proposed by B.A.Dubrovin and S.P.Novikov. Using the Dirac procedure of restriction of ...

A paradigm for describing dynamical systems that have both Hamiltonian and dissipative parts is presented. Features of generalized Hamiltonian systems and metric systems are combined to produce what are called metriplectic systems. The phase space for metriplectic systems is equipped with a bracket operator that has an antisymmetric Poisson bracket part and a symmetric dissipative part. Flows a...