论文标题
立方klein-gordon方程的呼吸溶液
Breather Solutions of the Cubic Klein-Gordon Equation
论文作者
论文摘要
我们获得了立方klein-gordon方程的实价，时间周期和径向对称解 \ partial_t^2 u-ΔU + m^2 u =γ（x）u^3 \ quad \ text {on} \ mathbb {r} \ times \ times \ mathbb {r}^3，\ end end {align}，它们位于空间中。这种“呼吸”溶液的各种家族都显示出来自任何给定的非平稳固定溶液的分叉。据作者所知，在三个空间维度上的弱点呼吸器的构建是一个新概念，并基于立方克莱因·戈登方程的重新制定，作为一个耦合的非线性helmholtz方程式系统，涉及涉及远处野外行为的适当条件。
We obtain real-valued, time-periodic and radially symmetric solutions of the cubic Klein-Gordon equation \begin{align} \partial_t^2 U - ΔU + m^2 U = Γ(x) U^3 \quad \text{on } \mathbb{R} \times \mathbb{R}^3, \end{align} which are weakly localized in space. Various families of such "breather" solutions are shown to bifurcate from any given nontrivial stationary solution. The construction of weakly localized breathers in three space dimensions is, to the author's knowledge, a new concept and based on the reformulation of the cubic Klein-Gordon equation as a system of coupled nonlinear Helmholtz equations involving suitable conditions on the far field behavior.
