Orbital stability of the sum of smooth solitons in the Degasperis-Procesi equation
Orbital stability of the sum of smooth solitons in the Degasperis-Procesi equation
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Degasperis-Procesi 方程中光滑孤子之和的轨道稳定性
DOI：
10.1016/j.matpur.2022.05.004
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发表时间：
2022
期刊：
影响因子：
--
通讯作者：
Wu, Qiliang
中科院分区：
文献类型：
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作者：
Li, Ji;Liu, Yue;Wu, Qiliang
摘要DeGasperis-Procesi(DP)方程是一个可积的Camassa-Holm型模型，作为浅水波单向传播的渐近近似。建立了包含N个光滑孤子的波列的L 2∩L∞轨道稳定性。主要困难来自于DP方程微妙的非局部结构。一个结果是，基于平移对称性引起的守恒量的DE方程的能量空间仅等价于L 2范数，它本身不能约束拉格朗日中的高阶非线性项。我们的补救方法是引入基于某些光滑初始条件的先验估计。此外，另一个结果是DP方程的非局部结构显著地使证明局部动量的单调性和正交化扰动的精化二次型的正定性变得复杂。
Abstract The Degasperis-Procesi (DP) equation is an integrable Camassa-Holm-type model as an asymptotic approximation for the unidirectional propagation of shallow water waves. This work is to establish the L 2∩ L∞ orbital stability of a wave train containing N smooth solitons which are well separated. The main difficulties stem from the subtle nonlocal structure of the DP equation. One consequence is that the energy space of the DE equation based on the conserved quantity induced by the translation symmetry is only equivalent to the L 2-norm, which by itself can not bound the higher-order nonlinear terms in the Lagrangian. Our remedy is to introduce a priori estimates based on certain smooth initial conditions. Moreover, another consequence is that the nonlocal structure of the DP equation significantly complicates the verification of the monotonicity of local momentum and the positive definiteness of a refined quadratic form of the orthogonalized perturbation.