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hamiltonian form
A new discrete isospectral problem is introduced, from which the coupled discrete KdV hierarchy is deduced and is written in its Hamiltonian form by means of the trace identity.
      
Obstacle to the reduction of nonholonomic systems to the Hamiltonian form
      
The Maxwell-Bloch equations are rewritten in Hamiltonian form without redefining the spatial and temporal variables.
      
A Hamiltonian form of the Maxwell-Bloch equation is found without redefining the spatiotemporal variables.
      
A three-dimensional equation of motion in the Hamiltonian form is derived.
      
The equations of dynamics of eddy-wave disturbances of two-dimensional stratified flows in an ideal incompressible fluid that are written in a Hamiltonian form are used to study the resonant interaction of waves of discrete and continuous spectra.
      
We consider generalizations of the standard Hamiltonian dynamics to complex dynamical variables and introduce the notions of real Hamiltonian form in analogy with the notion of real forms for a simple Lie algebra.
      
Transformations to replace the Galilean ones are obtained, the quasiparticle mechanics in a Hamiltonian form is deduced, and a Boltzmann-type transport equation (valid in the whole Brillouin zone) is derived.
      
In each case the relevant Hamiltonian form is established by making use of the trace identity.
      
Hamiltonian Form of the Maxwell Equations and Its Generalized Solutions
      
The case is considered that parts tv of the Hamiltonian form the observation level; it leads to systems with several temperatures.
      
The pair can also be written in bi-Hamiltonian form giving rise to an infinite hierarchy of coupled equations each of which is a Hamiltonian system.
      
Phenomenological field equations that describe isothermal chemical kinetics are cast into Hamiltonian form.
      
The method relies on the development of an orthogonal, symplectic change of variables to block triangular Hamiltonian form.
      
Quantum mechanics is cast into a classical Hamiltonian form in terms of a symplectic structure, not on the Hilbert space of state-vectors but on the more physically relevant infinite-dimensional manifold of instantaneous pure states.
      
We study partial differential equations of hamiltonian form and treat them as infinite-dimensional hamiltonian systems in a functional phase-space ofx-dependent functions.
      
We produce explicit solutions for some cases of the cohomogeneity one Einstein equations by finding generalised first integrals of the Hamiltonian form of these equations.
      
Using ideas from convex geometry, we prove a classification theorem, under suitable hypotheses, for superpotentials of the Hamiltonian form of the cohomogeneity one Ricci-flat equations.
      
The I-theorem for a system with known effective "Hamiltonian" and a system whose "Hamiltonian" form is not defined is proved.
      
On the other hand one can then proceed to give the Hamiltonian form up to the same order.
      
 

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