Rayleigh wave scattering at the foot of a mountain.
Deshwal, P.S., Mann, K.K. (1987)
International Journal of Mathematics and Mathematical Sciences
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Deshwal, P.S., Mann, K.K. (1987)
International Journal of Mathematics and Mathematical Sciences
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Bose, S.K., Debnath, L. (1981)
International Journal of Mathematics and Mathematical Sciences
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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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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...
Nikolai G. Kuznecov, Vladimir G. Maz'ya (2001)
Mathematica Bohemica
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The uniqueness theorem is proved for the linearized problem describing radiation and scattering of time-harmonic water waves by a vertical shell having an arbitrary horizontal cross-section. The uniqueness holds for all frequencies, and various locations of the shell are possible: surface-piercing, totally immersed and bottom-standing. A version of integral equation technique is outlined for finding a solution.
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.
Kellendonk, Johannes, Richard, Serge (2008)
Mathematical Physics Electronic Journal [electronic only]
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Frank, Rupert L. (2003)
Documenta Mathematica
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