Quasi-periodic solutions of the Heisenberg hierarchy

The Heisenberg hierarchy and its Hamiltonian structure are obtained respectively by use of the zero curvature equation trace identity. With help Lax matrix we introduce an algebraic curve $${\mathcal {K}}_{n}$$ arithmetic genus n, from which define meromorphic function $$\phi $$ straighten out all flows associated with under Abel–Jacobi coordinates. Finally, get explicit theta representations solutions for whole as a result asymptotic properties .