“…Our approach devised in the present work is substantially based on the results obtained earlier in [11,13] and explains completely the computational properties of multidimensional flows delivered earlier in [5,15,16]. The latter gives rise to some additional Hamiltonian properties of considered extended evolution flows studied earlier in [5,13], making use of the standard inverse scattering transform [2,3] and the formal symmetry reduction for the KP-hierarchy [15,16] of commuting operator flows. The latter gives rise to some additional Hamiltonian properties of considered extended evolution flows studied earlier in [5,13], making use of the standard inverse scattering transform [2,3] and the formal symmetry reduction for the KP-hierarchy [15,16] of commuting operator flows.…”