论文标题
在具有非传播电势的1D二次klein方程的修改散射上
On modified scattering for 1D quadratic Klein-Gordon equations with non-generic potentials
论文作者
论文摘要
我们考虑了小型全球时间解决方案对具有空间局部的，可变系数二次非线性和非传播线性电势的1D klein-gordon方程的渐近行为。这项工作的目的是继续研究解决方案的新型修饰散射行为的发生，涉及沿某些射线的衰减速率的对数减速。这种现象最终是由线性klein-gordon操作员的阈值共振引起的。以前是针对[51]中零电位的特殊情况发现的。本文考虑的Klein-Gordon模型是由在实际线路上经典标量场理论中引起的扭结解决方案的渐近稳定性问题的动机。
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 [51]. 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.
