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. Phys. Soc. 1009-1963/2006/15(09)/1919-08 and IOP Publishing Ltd Chinese Physics The quadratic -form identity for constructing Hamiltonian structures of the Guo hierarchy Dong Huan-He() and Zhang Ning ...
systems are derived. In order to look for the Hamiltonian structure of such integrable systems, a quadratic -form identity is created in the present paper whose special case is just the trace identity ...
is given. Also, the trace identity is extended to the quadratic -form identity and the Hamiltonian structures of the NLS-MKdV hierarchy and integrable coupling of NLS-MkdV hierarchy are obtained ...
by employing the constructed quadratic identity . PACS numbers: 05.45.Yv, 02.30.Jr Key words: integrable coupling, Hamiltonian structure , trace identity , quadratic identity 1 Introduction the fundamental research ...
are Liouville-integrable, whose Hamiltonian structures are derived by making use of the quadratic -form identity and the γ formula (i.e. the computational formula on the constant γ appeared in the trace identity ...
to obtaining the Tu hierarchy. By making use of the extended trace identity , the Hamiltonian structure of the Tu hierarchy is constructed . Furthermore, we apply the quadratic -form identity to the integrable ...
be reduced to computing formula of constant γ in the trace identity . As application, a new Liouville integrable hierarchy which possess bi- Hamiltonian structure and generalized Burgers hierarchy are derived ...
and thus implemented on a variety of competing quantum computing platforms. This representation requires translating the scoring function used in traditional approaches into a quadratic Hamiltonian where ...
asymptotics of a particular class of random Hamiltonians , introduced in the following way: Starting from an infinite graph, one considers subgraphs defined by a percolation process, that is, by deleting sites ...
on infinite-dimensional stable and unstable subspaces [2]. Accordingly, we shall extend our theory in a subsequent project to Hamiltonian partial differential equations as in [6]. The paper is structured ...
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