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pro vyhledávání: '"Soffer, Avy"'
In the present paper we consider global solutions of a class of non-linear wave equations of the form \begin{equation*} \Box u= N(x,t,u)u, \end{equation*} where the nonlinearity~$ N(x,t,u)u$ is assumed to satisfy appropriate boundedness assumptions.
Externí odkaz:
http://arxiv.org/abs/2409.05272
Autor:
Soffer, Avy
I present a review of the recent advancements in scattering theory, which provides a unified approach to studying dispersive and hyperbolic equations with general interaction terms and data. These equations encompass time-dependent potentials, as wel
Externí odkaz:
http://arxiv.org/abs/2408.14269
Autor:
Soffer, Avy, Stewart, Gavin
We study the large-time behavior of global energy class solutions of the one dimensional nonlinear Schr\"odinger equation with a general localized potential term and a defocusing nonlinear term. By using a new type of interaction Morawetz estimate lo
Externí odkaz:
http://arxiv.org/abs/2402.11366
Autor:
Soffer, Avy, Wu, Xiaoxu
We develop an approach to scattering theory for generalized $N$-body systems. In particular we consider a general class of three quasi-particle systems, for which we prove Asymptotic Completeness.
Comment: 82 pages, 3 figures. Comments welcome!
Comment: 82 pages, 3 figures. Comments welcome!
Externí odkaz:
http://arxiv.org/abs/2309.10178
We study the bi-laplacian Schr\"odinger equation with a general interaction term, which can be either linear or nonlinear, and is time-dependent. We prove that the global solutions for this equation are asymptotically given by a free wave and a weakl
Externí odkaz:
http://arxiv.org/abs/2308.06856
This paper is devoted to studying time decay estimates of the solution for Beam equation (higher order type wave equation) with a potential $$u_{t t}+\big(\Delta^2+V\big)u=0, \,\ u(0, x)=f(x),\ u_{t}(0, x)=g(x)$$ in dimension three, where $V$ is a re
Externí odkaz:
http://arxiv.org/abs/2307.16428
Autor:
Soffer, Avy, Wu, Xiaoxu
We consider the Schr\"odinger equation with a general interaction term, which is localized in space, for radially symmetric initial data in $n$ dimensions, $n\geq5$. The interaction term may be space-time dependent and nonlinear. Assuming that the so
Externí odkaz:
http://arxiv.org/abs/2304.04245
Autor:
Soffer, Avy, Wu, Xiaoxu
We give a proof of Local Decay Estimates for Schr\"odinger type equations, which is based on the knowledge of Asymptotic Completeness (AC). This approach extends to time dependent potential perturbations, as it does not rely on Resolvent Estimates or
Externí odkaz:
http://arxiv.org/abs/2211.00500
Autor:
Soffer, Avy, Wu, Xiaoxu
We construct solutions of Schr\"odinger equations which have asymptotic self similar solutions as time goes to infinity. Also included are situations with two-bubbles. These solutions are global, with constant non-zero $L^2$ norm, and are stable. As
Externí odkaz:
http://arxiv.org/abs/2205.14765