Abstract
Standard eikonal methods for the asymptotic analysis of coupled linear wave equations may fail when two eigenvalues of a matrix (the dispersion matrix) associated with the wave operator are both small in the same region of wave phase space. In this region the two eikonal modes associated with the two small eigenvalues are coupled, leading to a process called linear mode conversion or Landau-Zener coupling. A theory of linear mode conversion is presented in which geometric structure is emphasized. This theory is then used to identify the most generic type of mode conversion which occurs in one dimension. Finally, a general solution for this generic mode conversion problem is derived by transforming an arbitrary equation exhibiting generic mode conversion into an easily solvable normal form. This solution is given as a connection rule, with which one may continue standard eikonal wave solutions through mode conversion regions.
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