排序方式: 共有57条查询结果,搜索用时 125 毫秒
1.
In this paper, we present the multi-component Novikov equation and derive it's bi-Hamiltonian structure. 相似文献
2.
We address the problem of the separation of variables for the Hamilton–Jacobi equation within the theoretical scheme of bi-Hamiltonian geometry. We use the properties of a special class of bi-Hamiltonian manifolds, called N manifolds, to give intrisic tests of separability (and Stäckel separability) for Hamiltonian systems. The separation variables are naturally associated with the geometrical structures of the N manifold itself. We apply these results to bi-Hamiltonian systems of the Gel'fand–Zakharevich type and we give explicit procedures to find the separated coordinates and the separation relations. 相似文献
3.
Attilio Meucci 《Mathematical Physics, Analysis and Geometry》2001,4(2):131-146
We present the bi-Hamiltonian structure of Toda3, a dynamical system studied by Kupershmidt as a restriction of the discrete KP hierarchy. We derive this structure by a suitable reduction of the set of maps from Z
d
to GL(3,R), in the framework of Lie algebroids. 相似文献
4.
Based on a general isospectral problem of fractional order and the fractional quadratic-form identity by Yue and Xia, the new integrable coupling of fractional coupled Burgers hierarchy and its fractional bi-Hamiltonian structures are obtained. 相似文献
5.
《Communications in Nonlinear Science & Numerical Simulation》2014,19(7):2228-2233
By solving the zero-curvature equation associated with a 3 × 3 matrix spectral problem, a super hierarchy of coupled derivative nonlinear Schrödinger equations is proposed. The corresponding super bi-Hamiltonian structures are established by means of the super trace identity. Then, we derive infinite conservation laws of the super coupled derivative nonlinear Schrödinger equation with the aid of spectral parameter expansions. 相似文献
6.
We introduce nonlocal flows that commute with those of the classical Toda hierarchy. We define a logarithm of the difference Lax operator and use it to obtain a Lax representation of the new flows. 相似文献
7.
We discuss the relationship between the representation of an integrable system as an L-A-pair with a spectral parameter and the existence of two compatible Hamiltonian representations of this system. We consider examples of compatible Poisson brackets on Lie algebras, as well as the corresponding integrable Hamiltonian systems and Lax representations. 相似文献
8.
We introduce a bi-Hamiltonian hierarchy on the loop-algebra of
endowed with a suitable Poisson pair. It gives rise to the usual Camassa–Holm (CH) hierarchy by means of a bi-Hamiltonian reduction, and its first nontrivial flow provides a three-component extension of the CH equation. 相似文献
9.
ZHANG Yu-Feng 《理论物理通讯》2008,50(11):1021-1026
A new Lie algebra G of the Lie algebra sl(2) is constructed with complex entries whose structure constants are real and imaginary numbers. A loop algebra G corresponding to the Lie algebra G is constructed, for which it is devoted to generating a soliton hierarchy of evolution equations under the framework of generalized zero curvature equation which is derived from the compatibility of the isospectral problems expressed by Hirota operators. Finally, we decompose the Lie algebra G to obtain the subalgebras G1 and G2. Using the G2 and its one type of loop algebra G2, a Liouville integrable soliton hierarchy is obtained, furthermore, we obtain its bi-Hamiltonian structure by employing the quadratic-form identity. 相似文献
10.
Stephen C. Anco Shahid Mohammad Thomas Wolf Chunrong Zhu 《Journal of Nonlinear Mathematical Physics》2016,23(4):573-606
A one-parameter generalization of the hierarchy of negative flows is introduced for integrable hierarchies of evolution equations, which yields a wider (new) class of non-evolutionary integrable nonlinear wave equations. As main results, several integrability properties of these generalized negative flow equation are established, including their symmetry structure, conservation laws, and bi-Hamiltonian formulation. (The results also apply to the hierarchy of ordinary negative flows). The first generalized negative flow equation is worked out explicitly for each of the following integrable equations: Burgers, Korteweg-de Vries, modified Korteweg-de Vries, Sawada-Kotera, Kaup-Kupershmidt, Kupershmidt. 相似文献