论文标题
在Degasperis-Procesi方程中平稳的周期性流动波的稳定性
Stability of smooth periodic traveling waves in the Degasperis-Procesi equation
论文作者
论文摘要
我们得出了用于degasperis-Procesi（DP）方程中平滑周期波的精确能量稳定性标准。与Camassa-Holm（CH）方程相比，相关的Hessian操作员的负特征值的数量变化了光滑的Perodic波的存在区域。我们利用了两个参数的周期函数的属性，以便为固定周期的平滑周期性波的家族获得平滑的存在曲线。能量稳定性条件是在该存在曲线的一部分上得出的，该曲线对应于Hessian操作员的一个或两个负特征值。我们在数值上表明，能量稳定性条件在曲线的任一部分都得到满足，并在分析上证明其在平滑周期波的存在区域的边界附近。
We derive a precise energy stability criterion for smooth periodic waves in the Degasperis--Procesi (DP) equation. Compared to the Camassa-Holm (CH) equation, the number of negative eigenvalues of an associated Hessian operator changes in the existence region of smooth perodic waves. We utilize properties of the period function with respect to two parameters in order to obtain a smooth existence curve for the family of smooth periodic waves of a fixed period. The energy stability condition is derived on parts of this existence curve which correspond to either one or two negative eigenvalues of the Hessian operator. We show numerically that the energy stability condition is satisfied on either part of the curve and prove analytically that it holds in a neighborhood of the boundary of the existence region of smooth periodic waves.
