SEPARATION OF VARIABLES IN THE KRAMERS EQUATION

@article{Zhdanov1999SEPARATIONOV,
  title={SEPARATION OF VARIABLES IN THE KRAMERS EQUATION},
  author={R. Zhdanov and Alexander Zhalij},
  journal={Journal of Physics A},
  year={1999},
  volume={32},
  pages={3851-3863}
}
We consider the problem of separation of variables in the Kramers equation admitting a non-trivial symmetry group. Provided the external potential V(x) is at most quadratic, a complete solution of the problem of separation of variables is obtained. Furthermore, we construct solutions of the Kramers equation with separated variables in explicit form. 
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References

SHOWING 1-10 OF 20 REFERENCES
Symmetry classification and exact solutions of the Kramers equation
The complete classification of Lie symmetries for the Kramers equation is described. Group invariance under infinitesimal transformations is used to generate a wide class of exact solutions. Some of
Symmetry analysis of the Kramers equation
Abstract The complete classification of Lie symmetries for the Kramers equation is described. Also some Q -conditional symmetry properties of this equation have been investigated. The Q -conditional
Separation of variables in (1+2)-dimensional Schrödinger equations
Using our classification of separable Schrodinger equations with two space dimensions published in J. Math. Phys. 36, 5506 (1995) we give an exhaustive description of the coordinate systems providing
On the new approach to variable separation in the time-dependent Schr\
We suggest an effective approach to separation of variables in the Schrodinger equation with two space variables. Using it we classify inequivalent potentials V(x1,x2) such that the corresponding
Orthogonal and non-orthogonal separation of variables in the wave equation utt-uxx+V(x)u=0utt-uxx+V(x)u=0
We develop a direct approach to the separation of variables in partial differential equations. Within the framework of this approach, the problem of the separation of variables in the wave equation
Symmetry and Separation of Variables
Editor's statement Section editor's statement Preface 1. The Helmholtz equation 2. The Schrodinger and heat equations 3. The three-variable Helmholtz and Laplace equations 4. The wave equation 5. The
Brownian motion in a field of force and the diffusion model of chemical reactions
Abstract A particle which is caught in a potential hole and which, through the shuttling action of Brownian motion, can escape over a potential barrier yields a suitable model for elucidating the
Handbook of Stochastic Methods (Berlin: Springer
  • 1985
Symmetry and Separation of Variables (Massachusetts: Addison-Wesley
  • 1977
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