Spectral stability of smooth solitary waves for the Degasperis-Procesi equation
Spectral stability of smooth solitary waves for the Degasperis-Procesi equation
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Degasperis-Procesi 方程的平滑孤立波的谱稳定性
DOI：
10.1016/j.matpur.2020.08.003
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发表时间：
2020
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
Degasperis-Procesi方程是浅水波浪主要向一个方向传播的近似欧拉方程模型。该模型方程类似于二维不可压缩无旋转欧拉方程的Camassa-Holm近似，具有相同的渐近精度，并且与双哈密顿结构完全可积。本文在实线上建立了Degasperis-Procesi方程的局域光滑孤子的存在性和谱稳定性结果。稳定性证明主要依赖于Degasperis-Procesi方程局部哈密顿量二阶变分导数对应的线性算子的精细谱分析。
The Degasperis-Procesi equation is an approximating model of shallow-water wave propagating mainly in one direction to the Euler equations. Such a model equation is analogous to the Camassa-Holm approximation of the two-dimensional incompressible and irrotational Euler equations with the same asymptotic accuracy, and is completely integrable with the bi-Hamiltonian structure. In the present study, we establish existence and spectral stability results of localized smooth solitons to the Degasperis-Procesi equation on the real line. The stability proof relies essentially on refined spectral analysis of the linear operator corresponding to the second-order variational derivative of the local Hamiltonian of the Degasperis-Procesi equation.