Displaying similar documents to “Scattering Matrix for the Reflection-Transmission Problem in a Viscoelastic Medium”

Wave Operators for Defocusing Matrix Zakharov-Shabat Systems with Pnonvanishing at Infinity

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.

On uniqueness in electromagnetic scattering from biperiodic structures

Armin Lechleiter, Dinh-Liem Nguyen (2013)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

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Consider time-harmonic electromagnetic wave scattering from a biperiodic dielectric structure mounted on a perfectly conducting plate in three dimensions. Given that uniqueness of solution holds, existence of solution follows from a well-known Fredholm framework for the variational formulation of the problem in a suitable Sobolev space. In this paper, we derive a Rellich identity for a solution to this variational problem under suitable smoothness conditions on the material parameter....

Scattering theory for a nonlinear system of wave equations with critical growth

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...

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...