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21.
Compatible Nonlocal Poisson Brackets of Hydrodynamic Type and Integrable Hierarchies Related to Them
We construct integrable bi-Hamiltonian hierarchies related to compatible nonlocal Poisson brackets of hydrodynamic type and solve the problem of the canonical form for a pair of compatible nonlocal Poisson brackets of hydrodynamic type. A system of equations describing compatible nonlocal Poisson brackets of hydrodynamic type is derived. This system can be integrated by the inverse scattering problem method. Any solution of this integrable system generates integrable bi-Hamiltonian systems of hydrodynamic type according to explicit formulas. We construct a theory of Poisson brackets of the special Liouville type. This theory plays an important role in the construction of integrable hierarchies. 相似文献
22.
推广的AKNS方程族 总被引:3,自引:0,他引:3
本文得出的可积方程族,具有双 Hamilton结构,含 5个因变数ui,i=1,2,…,5.当u3=u4=u5=0时,它约化为 AKNS族,故称之为推广的 AKNS族. 相似文献
23.
The Neumann system on the two-dimensional sphere is used as a tool to convey some ideas on the bi-Hamiltonian standpoint on separation of variables. We show that from this standpoint, its separation coordinates and its integrals of motion can be found systematically. 相似文献
24.
With the help of the zero-curvature equation and the super trace identity, we derive a super extension of the Kaup-Newell hierarchy associated with a 3 × 3 matrix spectral problem and establish its super bi-Hamiltonian structures. Furthermore, infinite conservation laws of the super Kaup Newell equation are obtained by using spectral parameter expansions. 相似文献
25.
With the help of the zero-curvature equation and the super trace identity, we derive a super extension of the Kaup--Newell hierarchy associated with a 3×3 matrix spectral problem and establish its super bi-Hamiltonian structures. Furthermore, infinite conservation laws of the super Kaup-Newell equation are obtained by using spectral parameter expansions. 相似文献
26.
We have proved that any 3-dimensional dynamical system of ordinary differential equations (in short, 3D ODE) with time-independent
invariants can be rewritten as Hamiltonian systems with respect to generalized Poisson brackets and the Hamiltonians are these
invariants. As an example, we discuss the Kermack-Mckendrick model for epidemics in detail. The results we obtained are generalization
of those obtained by Y. Nutku.
First Received Nov. 22, 1993 相似文献
27.
A difference Ha-miltonian operator with three arbitrary constants is presented. When the arbitrary constants -in the Hamiltonian operator are suitably chosen, a pair of Hamiltonian operators are given. The resulting Hamiltonian pair yields a difference hereditary operator. Using Magri scheme of bi-Hamiltonian formulation, a hierarchy of the generalized Toda lattice equations is constructed. Finally, the discrete zero curvature representation is given for the resulting hierarchy. 相似文献
28.
《数学物理学报(B辑英文版)》1999,19(5):481-486
A united model of both the TM hierarchy and the coupled KdV hierarchy is proposed. By using the trace identity, the bi-Hamiltonian structure of the corresponding hierarchy is established. The isospectral problem is nonlinearized as a new completely integrable Hamiltonian system in Liouville sense. 相似文献
29.
A novel hierarchy of differential integral equations and their generalized bi-Hamiltonian structures
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With the aid of the zero-curvature equation, a novel integrable hierarchy of nonlinear evolution equations associated with a 3 x 3 matrix spectral problem is proposed. By using the trace identity, the bi-Hamiltonian structures of the hierarchy are established with two skew-symmetric operators. Based on two linear spectral problems, we obtain the infinite many conservation laws of the first member in the hierarchy. 相似文献
30.
O. I. Mokhov 《Functional Analysis and Its Applications》2003,37(2):103-113
We reduce an arbitrary pair of compatible nonlocal Poisson brackets of hydrodynamic type generated by metrics of constant Riemannian curvature (compatible Mokhov–Ferapontov brackets) to a canonical form, find an integrable system describing all such pairs, and, for an arbitrary solution of this integrable system, i.e., for any pair of compatible Poisson brackets in question, construct (in closed form) integrable bi-Hamiltonian systems of hydrodynamic type possessing this pair of compatible Poisson brackets of hydrodynamic type. The corresponding special canonical forms of metrics of constant Riemannian curvature are considered. A theory of special Liouville coordinates for Poisson brackets is developed. We prove that the classification of these compatible Poisson brackets is equivalent to the classification of special Liouville coordinates for Mokhov–Ferapontov brackets. 相似文献