## 60 Citations

The anisotropic Calder{ó}n problem on 3-dimensional conformally St{ä}ckel manifolds

- Mathematics
- 2019

Conformally St{a}ckel manifolds can be characterized as the class of n-dimensional pseudo-Riemannian manifolds (M, G) on which the Hamilton-Jacobi equation G($\nabla$u, $\nabla$u) = 0 for null…

THE EQUIVALENCE PROBLEM FOR ORTHOGONALLY SEPARABLE WEBS ON SPACES OF CONSTANT CURVATURE

- Mathematics
- 2011

This thesis is devoted to creating a systematic way of
determining all inequivalent orthogonal coordinate systems which
separate the Hamilton-Jacobi equation for a given natural
Hamiltonian defined…

On Darboux's approach to R-separability of variables I. Isothermic metrics and Dupin-cyclidic metrics

- Mathematics
- 2011

We discuss the problem of R-separability (separability of variables with a fac- tor R) in the stationary Schrodinger equation on n-dimensional Riemann space. We follow the approach of Gaston Darboux…

From Jacobi problem of separation of variables to theory of quasipotential Newton equations

- Mathematics
- 2009

AbstractOur solution to the Jacobi problem of finding separation variables for natural Hamiltonian systems H = ½p2 + V(q) is explained in the first part of this review. It has a form of an effective…

$R$-separable coordinates for three-dimensional complex Riemannian spaces

- Mathematics
- 1978

We classify all R-separable coordinate systems for the equations V.g 1 /112aj(g1l2gujai~= 0 and .. IgUaiWajOW= 0 with special emphasis on nonorthogonal coordinates, and give a group-theoretic…

Classification of the Orthogonal Separable Webs for the Hamilton-Jacobi and Klein-Gordon Equations on 3-Dimensional Minkowski Space

- MathematicsSymmetry, Integrability and Geometry: Methods and Applications
- 2022

We review a new theory of orthogonal separation of variables on pseudo-Riemannian spaces of constant zero curvature via concircular tensors and warped products. We then apply this theory to…

Separability of PDE

- PhysicsDrop Heating and Evaporation: Analytical Solutions in Curvilinear Coordinate Systems
- 2020

This chapter is devoted to analyse conditions and methods for PDE separation and among the several available techniques to solve Partial Differential Equations (PDE), separation of variable is generally the most valuable one since it may yield solutions in a form that is easily implementable for routine calculations.

Separability of the Planar 1/ρ2 Potential in Multiple Coordinate Systems

- PhysicsSymmetry
- 2020

This work examines another potential, for which the Schrodinger equation is separable in both cylindrical and parabolic coordinates: a $z-independent $V\propto 1/\rho^{2}=1/(x^2}+y^{2})$ in three dimensions.