Abstract The eigenvalue problem of an infinite-dimensional Hamiltonian operator appearing in the isotropic plane magnetoelectroelastic solids is studied. First, all the eigenvalues and their eigenfunctions in a rectangular domain are solved directly. Then the completeness of the eigenfunction system is proved, which offers a theoretic guarantee of the feasibility of variable separation method based on a Hamiltonian system for isotropic plane magnetoelectroelastic solids. Finally, the general solution for the equation in the rectangular domain is obtained by using the symplectic Fourier expansion method.
Received: 01 January 2008
Revised: 21 February 2008
Accepted manuscript online:
Fund: Project supported by
the National Natural Science Foundation of China (Grant No
10562002), the Natural Science Foundation of Inner Mongolia, China
(Grant No 200508010103), the Specialized Research Fund for the
Doctoral Program of Higher Education of China (Grant No 20070126002)
and the Inner Mongolia University Doctoral Scientific Research
Starting Foundation.
Cite this article:
Hou Guo-Lin(侯国林) and Alatancang(阿拉坦仓) On the feasibility of variable separation method based on Hamiltonian system for plane magnetoelectroelastic solids 2008 Chin. Phys. B 17 2753
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