On Modified Scattering for 1D Quadratic Klein–Gordon Equations With Non-Generic Potentials
On Modified Scattering for 1D Quadratic Klein–Gordon Equations With Non-Generic Potentials
复制标题
具有非泛势的一维二次克莱因-戈登方程的修正散射
DOI：
10.1093/imrn/rnac010
复制
发表时间：
2022
影响因子：
1
通讯作者：
Soffer, Avy
中科院分区：
文献类型：
--
作者：
Lindblad, Hans;Lührmann, Jonas;Schlag, Wilhelm;Soffer, Avy
考虑一类具有空间局域变系数二次非线性和非一般线性势的一维Klein-Gordon方程的全局小时间解的渐近行为。这项工作的目的是继续研究溶液的一种新的修正散射行为的发生，该行为涉及沿某些射线的衰减率的对数减慢。这种现象最终是由线性Klein-Gordon算子的阈值共振引起的。它以前是为中零电势的特殊情况而发现的。本文所考虑的Klein-Gordon模型是由实线上经典标量场论中的扭结解的渐近稳定性问题所激发的。
We consider the asymptotic behavior of small global-in-time solutions to a 1D Klein–Gordon equation with a spatially localized, variable coefficient quadratic nonlinearity and a non-generic linear potential. The purpose of this work is to continue the investigation of the occurrence of a novel modified scattering behavior of the solutions that involves a logarithmic slow-down of the decay rate along certain rays. This phenomenon is ultimately caused by the threshold resonance of the linear Klein–Gordon operator. It was previously uncovered for the special case of the zero potential in . The Klein–Gordon model considered in this paper is motivated by the asymptotic stability problem for kink solutions arising in classical scalar field theories on the real line.