Affiliation:
1. School of Mathematics and Statistics, Xinyang Normal University , 237 Nanhu Road , Xinyang , Henan 464000 , China
Abstract
Abstract
The Heisenberg hierarchy and its Hamiltonian structure are derived respectively by virtue of the zero-curvature equation and the trace identity. With the help of the Lax matrix, we introduce an algebraic curve
K
n
${\mathcal{K}}_{n}$
of arithmetic genus n, from which we define meromorphic function ϕ and straighten out all of the flows associated with the Heisenberg hierarchy under the Abel–Jacobi coordinates. Finally, we achieve the explicit theta function representations of solutions for the whole Heisenberg hierarchy as a result of the asymptotic properties of ϕ.
Funder
National Natural Science Foundation of China
Key Scientific Research Projects of Henan Institution of Higher Education
Nanhu Scholars Program for Young Scholars of Xinyang Normal University
Subject
Applied Mathematics,General Physics and Astronomy,Mechanics of Materials,Engineering (miscellaneous),Modelling and Simulation,Computational Mechanics,Statistical and Nonlinear Physics
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