论文标题
$ ϕ^{4n} $的轨道稳定性和周期性波解决方案的不稳定性 - 型号
Orbital stability and instability of periodic wave solutions for $ϕ^{4n}$-models
论文作者
论文摘要
在这项工作中，我们研究了所有$ n \ in \ mathbb {n} $的一般$ ϕ^{4n} $的特定周期性波解决方案的轨道稳定性/不稳定性。这个周期性解决方案家族在相应的阶段肖像中围绕起点绕，并且在常规案例中，（从适当的意义上）与Aperiodic的扭结解决方案相关联，该解决方案将状态$ - \ tfrac {1} {2} {2} $与$ \ tfrac {1} {1} {2} {2} $相关。在旅行案例中，我们证明了所有$ n \ in \ mathbb {n} $中的整个能量空间中的轨道不稳定性，而在常规案例中，我们证明，在某些额外的奇偶校验假设下，这些解决方案对于所有$ n \ in \ Mathbb {n} $ in \ Mathbb in \ Mathbb in \ Mathbb in \ n \ n \ n \ n} $。
In this work we study the orbital stability/instability in the energy space of a specific family of periodic wave solutions of the general $ϕ^{4n}$-model for all $n\in\mathbb{N}$. This family of periodic solutions are orbiting around the origin in the corresponding phase portrait and, in the standing case, are related (in a proper sense) with the aperiodic Kink solution that connect the states $-\tfrac{1}{2}$ with $\tfrac{1}{2}$. In the traveling case, we prove the orbital instability in the whole energy space for all $n\in\mathbb{N}$, while in the standing case we prove that, under some additional parity assumptions, these solutions are orbitally stable for all $n\in\mathbb{N}$.
