Approximate kink-kink solutions for the $\phi^{6}$ model in the low-speed limit
| Autor: | Moutinho, Abdon |
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| Rok vydání: | 2022 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | 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 $\phi^{6}$ model in dimension $1+1$. In this paper, we construct a sequence of approximate solutions $(\phi_{k}(v,t,x))_{k\in\mathbb{N}_{\geq 2}}$ for this nonlinear wave equation such that each function $\phi_{k}(v,t,x)$ 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 $\phi^{6}$ model. Comment: Submitted version. The first part of a series of two papers. Comments are welcome |
| Databáze: | arXiv |
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