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Asymptotic behaviour of the scattering phase for non-trapping obstacles

Veselin PetkovGeorgi Popov — 1982

Annales de l'institut Fourier

Let S ( λ ) be the scattering matrix related to the wave equation in the exterior of a non-trapping obstacle 𝒪 R n , n 3 with Dirichlet or Neumann boundary conditions on 𝒪 . The function s ( λ ) , called scattering phase, is determined from the equality e - 2 π i s ( λ ) = det S ( λ ) . We show that s ( λ ) has an asymptotic expansion s ( λ ) j = 0 c j λ n - j as λ + and we compute the first three coefficients. Our result proves the conjecture of Majda and Ralston for non-trapping obstacles.

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