论文标题
在$ ϕ^{6} $模型的扭结键冲突问题上
On the kink-kink collision problem of for the $ϕ^{6}$ model with low speed
论文作者
论文摘要
我们研究了两个扭结的碰撞的弹性，即传入的低速$ v \ in（0,1）$ in Dimension in Dimension $ 1+1 $称为$ ϕ^{6} $型号。我们证明，对于任何$ k \ in \ mathbb {n} $ $ v^{k}。$此手稿是我们以前的论文的延续，在该论文中，我们为$ ϕ^{6} $模型构建了一个序列$ ϕ_ {k} $。我们主要结果的证明依赖于我们以前的工作，调制分析以及在较大时间间隔内评估我们近似解决方案的精度的精制能量估算方法中使用的近似解决方案的使用。
We study the elasticity of the collision of two kinks with an incoming low speed $v\in (0,1)$ for the nonlinear wave equation in dimension $1+1$ known as the $ϕ^{6}$ model. We prove for any $k\in\mathbb{N}$ that if the incoming speed $v$ is small enough, then, after the collision, the two kinks will move away with a velocity $v_{f}$ such that $\vert v_{f}-v\vert\leq v^{k}$ and the energy of the remainder will also be smaller than $v^{k}.$ This manuscript is the continuation of our previous paper where we constructed a sequence $ϕ_{k}$ of approximate solutions for the $ϕ^{6}$ model. The proof of our main result relies on the use of the set of approximate solutions from our previous work, modulation analysis, and a refined energy estimate method to evaluate the precision of our approximate solutions during a large time interval.
