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By expanding the distribution function into Hermite-functions and into a Fourier-series, the Fokker-Planck-equation is transformed into a set of coupled equations for the expansion coefficients.
      
It is pointed out that chemical reactions which show an absorbing stationary state in the master-equation approach (e.g.
      
To get results for the Smoluchowski diffusion-equation we used the Dianoux-Volino-formalism which was generalized and applied to the Sack-diffusion-equation.
      
From a master-equation, which describes successive nearest-neighbour jumps of the particles, the concentration- and temperature-dependent tracer correlation factorft(c, T) is calculated by means of a mode-coupling approximation.
      
Numerical integrations of the Langevin-equation for the fluctuating light-field in a nonlinear resonator are presented.
      
With two approximations we reduce the resulting three-dimensional integral-equation into a one-dimensional integral-equation.
      
The influence of excited levels on nonlinear transport properties of a quantum dot weakly coupled to leads is studied using a master-equation approach.
      
In carrying out the linear stability analysis for these solutions, we have to treat the Schr?dinger-equation for a double-well potential.
      
This is done approximately by a supersymmetric approach which yields the eigenvalues and eigenfunctions of the Schr?dinger-equation.
      
The solution of the time-dependentDirac-Fock-Slater-equation is achieved via a set of coupled-channel equations with energy eigenvalues and matrix elements which are given by static SCF molecular many electron calculations.
      
Their derivation is reanalyzed here using standard techniques which lead to a master-equation.
      
Nonparabolic multivalley balance-equation approach to impact ionization: Application to wurtzite GaN
      
Balance-equation approach to terahertz-field-driven magnetotransport in semiconductors
      
Balance-equation approach to impact ionization induced by an intense terahertz radiation: Application to InAs/AlSb heterojunctio
      
In practice, for solving the local form HFKS-equation, we use the Car-Parrinello-like relaxation method and the Coulomb potentials are obtained by solving the Poisson equation under proper boundary conditions.
      
A two-dimensional, fully numerical approach to the four-component first-order Dirac-differential-equation utilizing the Finite-Element-Method (FEM) is employed for H2+ and Th 2179 +.
      
For this case we derive an approximation to the full Schr?dinger-equation, which allows the treatment of the composite systems in terms of product states.
      
Results of this kind may find application in the other fields in which an essential role is played by a wave-equation (like acoustics, seismology, geophysics, gravitation, elementary particle physics, etc.).
      
By considering important properties of the reference model describing a well-behaved nonlinear oscillator, it is possible to derive the error-equation, which is linear in the state variables.
      
Faddeev integral-equation treatment of elastic electron-hydrogen scattering
      
 

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