Small data scattering for nonlinear Schrödinger wave and Klein-Gordon equations

Makoto Nakamura; Tohru Ozawa

Displaying similar documents to “Small data scattering for nonlinear Schrödinger wave and Klein-Gordon equations”

Nonlinear Small Data Scattering for the Wave and Klein-Gordon Equation.

Hartmut Pecher (1984)

Mathematische Zeitschrift

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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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Scattering problem for nonlinear Schrödinger equations

Yoshio Tsutsumi (1985)

Annales de l'I.H.P. Physique théorique

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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.

Asymptotic behaviour of the scattering phase for non-trapping obstacles

Veselin Petkov, Georgi Popov (1982)

Annales de l'institut Fourier

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Let $S (λ)$ be the scattering matrix related to the wave equation in the exterior of a non-trapping obstacle $𝒪 \subset R^{n}$ , $n \geq 3$ with Dirichlet or Neumann boundary conditions on $\partial 𝒪$ . The function $s (λ)$ , called scattering phase, is determined from the equality $e^{- 2 π i s (λ)} = \det S (λ)$ . We show that $s (λ)$ has an asymptotic expansion $s (λ) \sim \sum_{j = 0}^{\infty} c_{j} λ^{n - j}$ as $λ \to + \infty$ and we compute the first three coefficients. Our result proves the conjecture of Majda and Ralston for non-trapping obstacles.

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 theory with two $L^{1}$ spaces : application to transport equations with obstacles

Mustapha Mokhtar-Kharroubi, Mohamed Chabi, Plamen Stefanov (1997)

Annales de la Faculté des sciences de Toulouse : Mathématiques

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On the real analyticity of the scattering operator for the Hartree equation

Changxing Miao, Haigen Wu, Junyong Zhang (2009)

Annales Polonici Mathematici

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We study the real analyticity of the scattering operator for the Hartree equation $i \partial_{t} u = - Δ u + u (V * | u | ²)$ . To this end, we exploit interior and exterior cut-off in time and space, together with a compactness argument to overcome difficulties which arise from absence of good properties as for the Klein-Gordon equation, such as the finite speed of propagation and ideal time decay estimate. Additionally, the method in this paper allows us to simplify the proof of analyticity of the scattering operator for the...