1+1维标量场的扭结网络
Kink networks for scalar fields in dimension 1+1
摘要：
本文考虑$1+1$维中的标量场方程，其正的外部势具有非退化孤立零点。我们构造了弱相互作用的纯多孤子，即在不同速度的情况下，解在时间上指数收敛到洛伦兹变换扭结的叠加。我们发现这些解在解的空间中形成一个$2K$维光滑流形，其中$K$是纽结的个数.我们证明了这个流形在对应于方程不变性的变换下是不变的，即时空平移和洛伦兹提升。
英文摘要：
We consider a scalar field equation in dimension $1+1$ with a positive external potential having non-degenerate isolated zeros. We construct weakly interacting pure multi-solitons, that is solutions converging exponentially in time to a superposition of Lorentz-transformed kinks, in the case of distinct velocities. We find that these solutions form a $2K$-dimensional smooth manifold in the space of solutions, where $K$ is the number of the kinks. We prove that this manifold is invariant under the transformations corresponding to the invariances of the equation, that is space-time translations and Lorentz boosts.
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