Asymptotic behaviour of the scattering phase for non-trapping obstacles
Annales de l'Institut Fourier, Volume 32 (1982) no. 3, p. 111-149

Let S(λ) be the scattering matrix related to the wave equation in the exterior of a non-trapping obstacle 𝒪R n , n3 with Dirichlet or Neumann boundary conditions on 𝒪. The function s(λ), called scattering phase, is determined from the equality e -2πis(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.

Soit S(λ) la matrice de diffusion, associée à l’équation des ondes dans l’extérieur d’un obstacle non-captif 𝒪R n , n3 avec condition de Dirichlet ou Neumann sur 𝒪. La fonction s(λ), dite phase de diffusion, est déterminée par l’égalité e -2πis(λ) = det S(λ). On démontre que s(λ) admet un développement asymptotique s(λ) j=0 c j λ n-j et on calcule les trois premiers coefficients. Notre résultat prouve la conjecture de Majda et Ralston pour des obstacles non-captifs.

@article{AIF_1982__32_3_111_0,
     author = {Petkov, Veselin and Popov, Georgi},
     title = {Asymptotic behaviour of the scattering phase for non-trapping obstacles},
     journal = {Annales de l'Institut Fourier},
     publisher = {Imprimerie Louis-Jean},
     address = {Gap},
     volume = {32},
     number = {3},
     year = {1982},
     pages = {111-149},
     doi = {10.5802/aif.882},
     zbl = {0476.35014},
     mrnumber = {85c:35070},
     language = {en},
     url = {http://www.numdam.org/item/AIF_1982__32_3_111_0}
}
Petkov, Veselin; Popov, Georgi. Asymptotic behaviour of the scattering phase for non-trapping obstacles. Annales de l'Institut Fourier, Volume 32 (1982) no. 3, pp. 111-149. doi : 10.5802/aif.882. http://www.numdam.org/item/AIF_1982__32_3_111_0/

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