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- Michael Kunzinger, Michael Oberguggenberger
- SIAM J. Math. Analysis
- 2000

We present an extension of the methods of classical Lie group analysis of differential equations to equations involving generalized functions (in particular: distributions). A suitable framework forâ€¦ (More)

The notion of singular reduction operators, i.e., of singular operators of nonclassical (conditional) symmetry, of partial differential equations in two independent variables is introduced. Allâ€¦ (More)

where (u, v) and (x, y) is a pair of null and (transverse) Cartesian coordinates respectively, and f denotes the profile function subject to the field equations. Hence the spacetime is flatâ€¦ (More)

- M. GroÃŸer, Michael Kunzinger, Roland Steinbauer, James A. Vickers
- 2009

We extend the construction of the authorsâ€™ paper of 2002 by introducing spaces of generalized tensor fields on smooth manifolds that possess optimal embedding and consistency properties with spacesâ€¦ (More)

- Michael Kunzinger, Michael Oberguggenberger, Roland Steinbauer, James A. Vickers
- 2004

Based on the concept of manifold valued generalized functions we initiate a study of nonlinear ordinary differential equations with singular (in particular: distributional) right hand sides in aâ€¦ (More)

Impulsive pp-waves are commonly described either by a distributional spacetime metric or, alternatively, by a continuous one. The transformation T relating these forms clearly has to beâ€¦ (More)

Colombeauâ€™s construction of generalized functions (in its special variant) is extended to a theory of generalized sections of vector bundles. As particular cases, generalized tensor analysis andâ€¦ (More)

- Michael Kunzinger, Roland Steinbauer, James A. Vickers
- 2008

The concept of generalized functions taking values in a differentiable manifold ([15, 19]) is extended to a functorial theory. We establish several characterization results which allow a globalâ€¦ (More)

Colombeauâ€™s construction of generalized functions (in its special variant) is extended to a theory of generalized sections of vector bundles. As particular cases, generalized tensor analysis andâ€¦ (More)

Generalized tensor analysis in the sense of Colombeauâ€™s construction is employed to introduce a nonlinear distributional pseudo-Riemannian geometry. In particular, after deriving severalâ€¦ (More)