Some new results in spectral and scattering theory of differential operators on
S. Agmon (1978-1979)
Séminaire Équations aux dérivées partielles (Polytechnique)
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S. Agmon (1978-1979)
Séminaire Équations aux dérivées partielles (Polytechnique)
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Roach, Gary F.
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Demontis, Francesco, der Mee, Cornelis van (2010)
Serdica Mathematical Journal
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2000 Mathematics Subject Classification: Primary: 34L25; secondary: 47A40, 81Q10. In this article we prove that the wave operators describing the direct scattering of the defocusing matrix Zakharov-Shabat system with potentials having distinct nonzero values with the same modulus at ± ∞ exist, are asymptotically complete, and lead to a unitary scattering operator. We also prove that the free Hamiltonian operator is absolutely continuous.
White, Denis A.W. (1992)
International Journal of Mathematics and Mathematical Sciences
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Changxing Miao, Youbin Zhu (2006)
Colloquium Mathematicae
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We consider scattering properties of the critical nonlinear system of wave equations with Hamilton structure ⎧uₜₜ - Δu = -F₁(|u|²,|v|²)u, ⎨ ⎩vₜₜ - Δv = -F₂(|u|²,|v|²)v, for which there exists a function F(λ,μ) such that ∂F(λ,μ)/∂λ = F₁(λ,μ), ∂F(λ,μ)/∂μ = F₂(λ,μ). By using the energy-conservation law over the exterior of a truncated forward light cone and a dilation identity, we get a decay estimate for...
Lars Hörmander (1976)
Mathematische Zeitschrift
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Veselin Petkov, Georgi Popov (1982)
Annales de l'institut Fourier
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Let be the scattering matrix related to the wave equation in the exterior of a non-trapping obstacle , with Dirichlet or Neumann boundary conditions on . The function , called scattering phase, is determined from the equality . We show that has an asymptotic expansion as and we compute the first three coefficients. Our result proves the conjecture of Majda and Ralston for non-trapping obstacles.
Günter Stolz, Thomas Poerschke (1993)
Mathematische Zeitschrift
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V. Chiadò Piat, M. Codegone (2003)
RACSAM
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In this paper, we consider a family of scattering problems in perforated unbounded domains Ω. We assume that the perforation is contained in a bounded region and that the holes have a ?critical? size. We study the asymptotic behaviour of the outgoing solutions of the steady-state scattering problem and we prove that an extra term appears in the limit equation. Finally, we obtain convergence results for scattering frequencies and solutions.