Global dynamics beyond the ground state energy for nonlinear dispersive equations

Kenji Nakanishi

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Displaying similar documents to “Global dynamics beyond the ground state energy for nonlinear dispersive equations”

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.

Dunkl-Schrödinger Equations with and without Quadratic Potentials

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.

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

Hartmut Pecher (1984)

Mathematische Zeitschrift

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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 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...

On L...-decay and scattering for nonlinear Klein-Gordon equations.

Philip Brenner (1982)

Mathematica Scandinavica

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On a Global Existence Theorem of Small Amplitude Solutions for Nonlinear Wave Equations in an Exterior Domain.

Yoshihiro Shibata, Yoshio Tsutsumi (1986)

Mathematische Zeitschrift

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Global Results for Solution to the Mass-Critical Schrödinger Equation with Convolution Nonlinearity in R^n Глобални резултати за решението на уравнението на шрьодингер с критична маса и нелинейност от конволюционен тип в R^n

Venkov, George, Genev, Hristo (2010)

Union of Bulgarian Mathematicians

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Георги Венков, Христо Генев - Разглеждаме един клас от L^2 - критични нелинейни уравнения на Шрьодингер в R^(1+n) с конволюционна нелинейност от тип Хартри. Целта ни е да установим локалното и глобално съществуване на решенията, както и коректност на задачата на Коши в достатъчно малка околност на нулата в пространството L^2 (R^n). Като естествено следствие на глобалните резултати ние доказваме съществуване на оператор на разсейване за малки начални условия. We are concerned...

On Space-Time Means Everywhere Defined Scattering Operators for Nonlinear Klein-Gordon Equations.

Philip Brenner (1984)

Mathematische Zeitschrift

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Scattering theory for Hartree type equations

Nakao Hayashi, Yoshio Tsutsumi (1987)

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

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

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 $ℝ^{n}$ with order $s < n / 2$ . The assumptions on the nonlinearities are described in terms of power behavior $p_{1}$ at zero and $p_{2}$ at infinity such as $1 + 4 / n \leq p_{1} \leq p_{2} \leq 1 + 4 / (n - 2 s)$ for NLS and NLKG, and $1 + 4 / (n - 1) \leq p_{1} \leq p_{2} \leq 1 + 4 / (n - 2 s)$ for NLW.