论文标题
Novikov方程的Peamons火车的轨道和渐近稳定性
Orbital and asymptotic stability of a train of peakons for the Novikov equation
论文作者
论文摘要
Novikov方程是具有立方非线性的可集成的Camassa-Holm型方程。该方程的最重要特征之一是存在Pearpon和多峰溶液的存在，即表现为孤子的峰值行进波。本文旨在证明Pearmon Trains解决方案的轨道和渐近稳定性，即多峰溶液，以便越来越有序的初始配置。此外，我们可以改善单个峰的轨道稳定性，以便在动量密度上删除非阴性假设。对于Pearmon火车的轨道稳定性也相同的结果，即在后一种情况下，我们还可以避免假设初始动量密度的非负性。最后，作为这些结果的推论，以及一些用于多峰溶液的位置和动量向量的渐近公式，我们获得了轨道和渐近稳定性，用于最初不是有序的多孔。
The Novikov equation is an integrable Camassa-Holm type equation with cubic nonlinearity. One of the most important features of this equation is the existence of peakon and multi-peakon solutions, i.e. peaked traveling waves behaving as solitons. This paper aims to prove both, the orbital and asymptotic stability of peakon trains solutions, i.e. multi-peakon solutions such that their initial configuration is increasingly ordered. Furthermore, we give an improvement of the orbital stability of a single peakon so that we can drop the non-negativity hypothesis on the momentum density. The same result also holds for the orbital stability for peakon trains, i.e. in this latter case we can also avoid assuming non-negativity of the initial momentum density. Finally, as a corollary of these results together with some asymptotic formulas for the position and momenta vectors for multi-peakon solutions, we obtain the orbital and asymptotic stability for initially not well-ordered multipeakons.
