Displaying similar documents to “Long range scattering and modified wave operators for Hartree equations”

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...

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.