INVARIANCE AND STABILITY OF THE PROFILE EQUATIONS OF GEOMETRIC OPTICS |
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| Authors: | Guy Metivier Jeffrey Raueh |
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| Institution: | Guy Mtivier Institut de Mathmatiques de Bordeaux, Universit de Bordeaux, CNRS Talence, France Jeffrey Rauch Department of Mathematics, University of Michigan, Ann Arbor, Michigan, USA |
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| Abstract: | The profile equations of geometric optics are described in a form invariant under the natural transformations of first order systems of partial differential equations. This allows us to prove that various strategies for computing profile equations are equivalent. We prove that if L generates an evolution on L 2 the same is true of the profile equations. We prove that the characteristic polynomial of the profile equations is the localization of the characteristic polynomial of the background operator at (y, ... |
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| Keywords: | geometric optics profile equation localisation vector bundles propagation cones |
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