Killing Tensors and Variable Separation for Hamilton-Jacobi and Helmholtz Equations
- 1 November 1980
- journal article
- Published by Society for Industrial & Applied Mathematics (SIAM) in SIAM Journal on Mathematical Analysis
- Vol. 11 (6) , 1011-1026
- https://doi.org/10.1137/0511089
Abstract
Summary:A PDE system is said to be of finite type if all possible derivatives at some order can be solved for in terms lower order derivatives. An algorithm for determining whether a system of finite type has solutions is outlined. The results are then applied to the problem of characterizing symmetric linear connections in two dimensions that possess homogeneous linear and quadratic integrals of motions, that is, solving Killing's equations of degree one and twoKeywords
This publication has 10 references indexed in Scilit:
- A precise definition of separation of variablesPublished by Springer Nature ,1980
- Separable components for three-dimensional complex riemannian spacesJournal of Differential Geometry, 1979
- Separable coordinates for four-dimensional Riemannian spacesCommunications in Mathematical Physics, 1978
- Mathematical Methods of Classical MechanicsPublished by Springer Nature ,1978
- The Group $O(4)$, Separation of Variables and the Hydrogen AtomSIAM Journal on Applied Mathematics, 1976
- Structural equations for Killing tensors of order two. IIJournal of Mathematical Physics, 1975
- On the Separation of Variables for the Laplace Equation $\Delta \psi + K^2 \psi = 0$ in Two- and Three-Dimensional Minkowski SpaceSIAM Journal on Mathematical Analysis, 1975
- The Fundamental Theorem on Quadratic First IntegralsProceedings of the National Academy of Sciences, 1946
- Separable Systems of StackelAnnals of Mathematics, 1934
- Orthogonal systems of hypersurfaces in a general Riemann spaceTransactions of the American Mathematical Society, 1923