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1.
In this paper, a new completely integrable system related to the complex spectral problem -φ xx+(i/4)wpx+(i/4)(wp)x+(1/4)vφ=iλφxand the constrained flows of the Boussinesq equations axe generated. According to the viewpoint of Hamiltonian mechanics, the Euler-Lagrange equations and the Legendre transformations, a reasonable Jacobi-Ostrogradsky coordinate system is obtained. Moreover, by means of the constrained conditions between the potentiaJ u, v and the eigenfunction φ, the involutive representations of the solutions for the Boussinesq equation hieraxchy axe given. 相似文献
2.
YANG Hong-Xiang CAO Wei-Li HOU Ying-Kun ZHU Xiang-Cai 《理论物理通讯》2008,50(9):593-597
By considering a new discrete isospectral eigenvalue problem, a hierarchy of lattice soliton equations of rational type are derived. It is shown that each equation in the resulting hierarchy is integrable in Liouville sense and possessing bi-Hamiltonian structure. Two types of semi-direct sums of Lie algebras are proposed, by using of which a practicable way to construct discrete integrable couplings is introduced. As applications, two kinds of discrete integrable couplings of the resulting system are worked out. 相似文献
3.
By considering a new discrete isospectral eigenvalue problem, a hierarchy of lattice soliton equations of rational type are derived. It is shown that each equation in the resulting hierarchy is integrable in Liouville sense and possessing
bi-Hamiltonian structure. Two types of semi-direct sums of Lie algebras are proposed, by using of which a practicable way to construct discrete integrable couplings is introduced. As
applications, two kinds of discrete integrable couplings of the
resulting system are worked out. 相似文献