Displaying similar documents to “Propagation of singularities in many-body scattering in the presence of bound states”

Recovering Asymptotics at Infinity of Perturbations of Stratified Media

Tanya Christiansen, Mark S. Joshi (2000)

Journées équations aux dérivées partielles

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We consider perturbations of a stratified medium ℝ x n - 1 × ℝ y , where the operator studied is c 2 ( x , y ) Δ . The function c is a perturbation of c 0 ( y ) , which is constant for sufficiently large | y | and satisfies some other conditions. Under certain restrictions on the perturbation c , we give results on the Fourier integral operator structure of the scattering matrix. Moreover, we show that we can recover the asymptotic expansion at infinity of c from knowledge of c 0 and the singularities of the scattering matrix at...

On the real analyticity of the scattering operator for the Hartree equation

Changxing Miao, Haigen Wu, Junyong Zhang (2009)

Annales Polonici Mathematici

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We study the real analyticity of the scattering operator for the Hartree equation i ∂ t u = - Δ u + u ( V * | u | ² ) . To this end, we exploit interior and exterior cut-off in time and space, together with a compactness argument to overcome difficulties which arise from absence of good properties as for the Klein-Gordon equation, such as the finite speed of propagation and ideal time decay estimate. Additionally, the method in this paper allows us to simplify the proof of analyticity of the scattering operator for the...

Asymptotic behaviour of the scattering phase for non-trapping obstacles

Veselin Petkov, Georgi Popov (1982)

Annales de l'institut Fourier

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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.