数学物理学报(英文版) ›› 2011, Vol. 31 ›› Issue (6): 2141-2158.doi: 10.1016/S0252-9602(11)60390-1

• 论文 • 上一篇    下一篇

INVARIANCE AND STABILITY OF THE PROFILE EQUATIONS OF GEOMETRIC OPTICS

Guy Métivier1|Jeffrey Rauch2   

  1. 1.Institut de Mathématiques de Bordeaux, Universit´e de Bordeaux, CNRS Talence, France;2.Department of Mathematics, University of Michigan, Ann Arbor, Michigan, USA
  • 收稿日期:2011-05-13 出版日期:2011-11-20 发布日期:2011-11-20

INVARIANCE AND STABILITY OF THE PROFILE EQUATIONS OF GEOMETRIC OPTICS

Guy Métivier1|Jeffrey Rauch2   

  1. 1.Institut de Mathématiques de Bordeaux, Universit´e de Bordeaux, CNRS Talence, France;2.Department of Mathematics, University of Michigan, Ann Arbor, Michigan, USA
  • Received:2011-05-13 Online:2011-11-20 Published:2011-11-20

摘要:

The profile equations of geometric optics are described in a form invariant un-der 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 L2 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, (y)) where Φ is the bak-
ground phase. We prove that the propagation cones of the profile equations are subsets of
the propagation cones of the background operator.

关键词: geometric optics, profile equation, localisation, vector bundles, propagation cones

中图分类号: 

  • 35L40