Displaying similar documents to “Wave Operators for Defocusing Matrix Zakharov-Shabat Systems with Pnonvanishing at Infinity”

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...

Scattering Matrix for the Reflection-Transmission Problem in a Viscoelastic Medium

Alessia Berti (2007)

Bollettino dell'Unione Matematica Italiana

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The reflection-transmission problem of time-harmonic waves in a viscoelastic, anisotropic and stratified solid is examined. The medium is supposed to occupy the whole space. The waves are sent either from upwards or downwards with oblique incidence. The scattering matrix is defined by generalizing the procedure followed in the scalar case, namely, when the solid is isotropic and the wave incidence is normal. Existence, uniqueness and properties of the scattering matrix are discussed. ...

Scattering of small solutions of a symmetric regularized-long-wave equation

Sevdzhan Hakkaev (2004)

Applicationes Mathematicae

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We study the decay in time of solutions of a symmetric regularized-long-wave equation and we show that under some restriction on the form of nonlinearity, the solutions of the nonlinear equation have the same long time behavior as those of the linear equation. This behavior allows us to establish a nonlinear scattering result for small perturbations.