论文标题
$ ϕ^{6} $模型的近似扭结解决方案在低速极限
Approximate kink-kink solutions for the $ϕ^{6}$ model in the low-speed limit
论文作者
论文摘要
该手稿是两篇论文系列中的第一组，研究了两个具有低速$ v $的矛盾的弹性和稳定性的问题，用于非线性波方程，称为$ 1+1 $ $ 1+1 $。在本文中，我们构建了一系列近似解决方案$（ϕ_ {k}（v，v，t，x））_ {k \ in \ mathbb {n} _ {n} _ {\ geq 2}} $对于这个非线性波方程$+\ infty。$本文中使用的方法不仅限于$ ϕ^{6} $模型。
This manuscript is the first of a series of two papers that study the problem of elasticity and stability of the collision of two kinks with low speed $v$ for the nonlinear wave equation known as the $ϕ^{6}$ model in dimension $1+1$. In this paper, we construct a sequence of approximate solutions $(ϕ_{k}(v,t,x))_{k\in\mathbb{N}_{\geq 2}}$ for this nonlinear wave equation such that each function $ϕ_{k}(v,t,x)$ converges in the energy norm to the traveling kink-kink with speed $v$ when $t$ goes to $+\infty.$ The methods used in this paper are not restricted only to the $ϕ^{6}$ model.
