共查询到20条相似文献,搜索用时 0 毫秒
1.
A recently proposed three-component Camassa-Holm equation is considered. It is shown that this system is a bi-Hamiltonian system. 相似文献
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In this paper, we present the multi-component Novikov equation and derive it's bi-Hamiltonian structure. 相似文献
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In this Letter we study the sine-Gordon and the Liouville hierarchies in laboratory coordinates from a bi-Hamiltonian point
of view. Besides the well-known local structure these hierarchies possess a second compatible nonlocal Poisson structure. 相似文献
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The noncommutative Toda hierarchy is studied with the help of Moyal deformation by a reduction on the non-commutative two dimensional Toda hierarchy. Further we generalize the noncommutative Toda hierarchy to the extended noncommutative Toda hierarchy. To survey on its integrability, we construct the bi-Hamiltonian structure and noncommutative conserved densities of the extended noncommutative Toda hierarchy by means of the R-matrix formalism. This extended noncommutative Toda hierarchy can be reduced to the extended multicomponent Toda hierarchy, extended ZN?-Toda hierarchy, extended Toda hierarchy respectively by reductions on Lie algebras. 相似文献
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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
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REN Wen-Xiu Alatancang 《理论物理通讯》2007,48(2):211-214
In the present paper, we identify the integrability of the third-order nonlinear evolution equation ut = (1/2)((uxz + u)^-2)z in a Hamiltonian viewpoint. We prove that the recursion operator obtained by S.Yu. Sakovich is hereditary, and then deduce a bi-Hamiltonian structure of the equation by using some decomposition of the hereditary operator. A hierarchy associated to the equation is also shown. 相似文献
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In the present paper, we identify the integrability of the third-order nonlinear evolution equation ut = (1/2)((uxx u)-2)x in a Hamiltonian viewpoint. We prove that the recursion operator obtained by S. Yu. Sakovich is hereditary, and then deduce a bi-Hamiltonian structure of the equation by using some decomposition of the hereditary operator. A hierarchy associated to the equation is also shown. 相似文献
8.
Roman G. Smirnov 《Letters in Mathematical Physics》1997,41(4):333-347
A method of generating a MMGD (Magri–Morosi-Gel'fand–Dorfman) bi-Hamiltonian structure leading to complete integrability of the associated Hamiltonian system is presented. The Hamiltonian formalism is defined in terms of the fundamental notions of the Poisson calculus. 相似文献
9.
Jafar Abedi-Fardad Ghorbanali Haghighatdoost 《Journal of Nonlinear Mathematical Physics》2017,24(2):149-170
We provide an alternative method for obtaining of compatible Poisson structures on Lie groups by means of the adjoint representations of Lie algebras. In this way we calculate some compatible Poisson structures on four dimensional and nilpotent six dimensional symplectic real Lie groups. Then using Magri-Morosi’s theorem we obtain new bi-Hamiltonian systems with four dimensional and nilpotent six dimensional symplectic real Lie groups as phase spaces. 相似文献
10.
Some two-component extensions of the modifiedμ-Camassa-Holm equation are proposed.We show that these systems admit Lax pairs and bi-Hamiltonian structures.Furthermore,we consider the blow-up phenomena for one of these extensions(2μmCH),and the periodic peakons of this system are derived. 相似文献
11.
Benito Hernández-Bermejo 《Physics letters. A》2010,374(6):836-1975
The problem of characterizing all new-time transformations preserving the Poisson structure of a finite-dimensional Poisson system is completely solved in a constructive way. As a corollary, this leads to a broad generalization of previously known results. Examples are given. 相似文献
12.
M. A. Oliver 《Foundations of Physics Letters》1991,4(4):337-350
The distribution of astronomical redshifts and the cosmic background radiation define a unique inertial reference frame. This paper contains an investigation of questions concerning quantum theory which arise with the introduction of a unique rest frame into spacetime. The Mössbauer effect, photon pair production, and photoelectric effect are treated together with photon scattering by a moving reflector and the Compton effect. Dirac's 1928 quantum theory of electrons is shown to yield its well-known energy spectrum for the hydrogen atom independently of the velocity of the atom relative to the rest frame.1. Address for the academic year 1990–91: 415 Graduate Studies Research Center, University of Georgia, Athens, Georgia 30602, USA. 相似文献
13.
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
14.
研究选取合适的准坐标简化完整系统Boltzmann-Hamel方程的问题.基于流形上的标架场理论,指出了定常构形空间中的准速度与标架场的联系,并从几何不变性的角度上导出了完整系统的Boltzmann-Hamel方程.证明了对于任意广义力为零的均匀构形空间、广义力不为零的零曲率构形空间,Boltzmann-Hamel方程均可以化简为可积分的形式,同时给出具体的简化方法并举例说明本方法的适用性.本文方法为寻找运动方程的解析解提供了一条新途径. 相似文献
15.
We survey some recent applications of the Differential Galois Theory of linear differential equations to the integrability (or solvability) of Dynamical Systems and Spectral Problems. 相似文献
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We present a computational method for determining the geometry of a class of three-dimensional invariant manifolds in non-autonomous (aperiodically time-dependent) dynamical systems. The presented approach can be also applied to analyse the geometry of 3D invariant manifolds in three-dimensional, time-dependent fluid flows. The invariance property of such manifolds requires that, at any fixed time, they are given by surfaces in R3. We focus on a class of manifolds whose instantaneous geometry is given by orientable surfaces embedded in R3. The presented technique can be employed, in particular, to compute codimension one (invariant) stable and unstable manifolds of hyperbolic trajectories in 3D non-autonomous dynamical systems which are crucial in the Lagrangian transport analysis. The same approach can also be used to determine evolution of an orientable ‘material surface’ in a fluid flow. These developments represent the first step towards a non-trivial 3D extension of the so-called lobe dynamics — a geometric, invariant-manifold-based framework which has been very successful in the analysis of Lagrangian transport in unsteady, two-dimensional fluid flows. In the developed algorithm, the instantaneous geometry of an invariant manifold is represented by an adaptively evolving triangular mesh with piecewise C2 interpolating functions. The method employs an automatic mesh refinement which is coupled with adaptive vertex redistribution. A variant of the advancing front technique is used for remeshing, whenever necessary. Such an approach allows for computationally efficient determination of highly convoluted, evolving geometry of codimension one invariant manifolds in unsteady three-dimensional flows. We show that the developed method is capable of providing detailed information on the evolving Lagrangian flow structure in three dimensions over long periods of time, which is crucial for a meaningful 3D transport analysis. 相似文献
20.
We propose a bi-Hamiltonian formulation of the Euler equation for the free n-dimensional rigid body moving about a fixed point. This formulation lives on the physical phase space so(n), and is different from the bi-Hamiltonian formulation on the extended phase space sl(n), considered previously in the literature. Using the bi-Hamiltonian structure on so(n), we construct new recursion schemes for the Mishchenko and Manakov integrals of motion. 相似文献