On the scattering in Gevrey classes for the subcritical Hartree and Schrödinger equations
Nakao Hayashi, Keiichi Kato, Pavel I. Naumkin (1998)
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
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Nakao Hayashi, Keiichi Kato, Pavel I. Naumkin (1998)
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
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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...
Mejjaoli, Hatem (2011)
Serdica Mathematical Journal
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2000 Mathematics Subject Classification: Primary 42A38. Secondary 42B10. The purpose of this paper is to study the dispersive properties of the solutions of the Dunkl-Schrödinger equation and their perturbations with potential. Furthermore, we consider a few applications of these results to the corresponding nonlinear Cauchy problems.
Yoshio Tsutsumi (1985)
Annales de l'I.H.P. Physique théorique
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Nakao Hayashi, Pavel I. Naumkin (1998)
Annales de l'I.H.P. Physique théorique
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Nakao Hayashi, Yoshio Tsutsumi (1987)
Annales de l'I.H.P. Physique théorique
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Makoto Nakamura, Tohru Ozawa (2002)
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
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Small data scattering for nonlinear Schrödinger equations (NLS), nonlinear wave equations (NLW), nonlinear Klein-Gordon equations (NLKG) with power type nonlinearities is studied in the scheme of Sobolev spaces on the whole space with order . The assumptions on the nonlinearities are described in terms of power behavior at zero and at infinity such as for NLS and NLKG, and for NLW.