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81.
Starting from a discrete spectral problem, a hierarchy of integrable lattice soliton equations is derived. It is shown that the hierarchy is completely integrable in the Liouville sense and possesses discrete bi-Hamiltonian structure. A new integrable
symplectic map and finite-dimensional integrable systems are given
by nonlinearization method. The binary Bargmann constraint gives
rise to a Bäcklund transformation for the resulting
integrable lattice equations. At last, conservation laws of the
hierarchy are presented. 相似文献
82.
Hamilton formalism and Noether symmetry for mechanico—electrical systems with fractional derivatives
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This paper presents extensions to the traditional calculus of variations for mechanico-electrical systems containing fractional derivatives.The Euler-Lagrange equations and the Hamilton formalism of the mechanico-electrical systems with fractional derivatives are established.The definition and the criteria for the fractional generalized Noether quasisymmetry are presented.Furthermore,the fractional Noether theorem and conseved quantities of the systems are obtained by virtue of the invariance of the Hamiltonian action under the infinitesimal transformations.An example is presented to illustrate the application of the results. 相似文献
83.
This paper analytically investigates the interaction of light
filaments generated by a femtosecond laser beam in air. It obtains the
Hamiltonian of a total laser field and interaction force between two
filaments with different phase shifts and crossing angles. The
property of the interaction force, which leads the attraction or
repulsion of filaments, is basically dependent on the phase shift
between filaments. The crossing angle between two filaments can only
determine the magnitude of the interaction force, but does not
change the property of the force. 相似文献
84.
根据物理量的可测实在性,应用二次型理论,一般地解决了3个质量与3个频率均不相同、坐标和动量各自具有全耦合谐振子系统的哈密顿量的可对角化问题,并具体给出了哈密顿量对角化的标准形. 相似文献
85.
86.
Jiangdan LiSuying Zhang 《Physics letters. A》2011,375(6):974-977
We provide a new insight into the relationship between the geometric property of the potential energy surface and chaotic behavior of 2D Hamiltonian dynamical systems, and give an indicator of chaos based on the geometric property of the potential energy surface by defining Mean Convex Index (MCI). We also discuss a model of unstable Hamiltonian in detail, and show our results in good agreement with HBLSL's (Horwitz, Ben Zion, Lewkowicz, Schiffer and Levitan) new Riemannian geometric criterion. 相似文献
87.
88.
89.
Guihua FeiSoon-Kyu Kim Tixiang Wang 《Journal of Mathematical Analysis and Applications》2002,267(2):665-678
In this paper, we study the existence of periodic solutions for classical Hamiltonian systems without the Palais-Smale condition. We prove that the information of the potential function contained in a finite domain is sufficient for the existence of periodic solutions. Moreover, we establish the existence of infinitely many periodic solutions without any symmetric condition on the potential function V. 相似文献
90.
We study the spectrum of Hamiltonians of charged multiparticle systems in a homogeneous magnetic field with a fixed sum P
of the pseudomomentum components and without it. We prove that if P
is fixed, then the spectrum of Hamiltonians is independent of the value of P
, while the spectrum without fixation of P
coincides with the spectrum with fixation and differs from the latter only by some additional infinite degeneration (this is a principal difference between problems with a homogeneous magnetic field and problems without any field in which the absence of any fixation of the total angular momentum results in covering the spectrum of the relative motion by a continuous spectrum). We find the continuous spectrum of the Hamiltonians and characterize the spectrum of Hamiltonians of two-cluster mutually noninteracting systems obtained by decomposing the original system in the state with a fixed value of P
. The last result is necessary for the study of the purely point spectrum. 相似文献