论文标题
扰动对Camassa-Holm方程中峰值周期性波的摄入量的生长，
Growth of perturbations to the peaked periodic waves in the Camassa-Holm equation,
论文作者
论文摘要
重新访问Camassa-Holm方程中的峰值周期波。线性化的演变方程是针对峰值周期波的扰动而得出的，并且线性化的不稳定性在$ h^1 $和$ w^{1，\ infty} $ norms中证明。 $ h^1 $中扰动的动力学与存在两个保守数量有关，并且由于这些保守数量而在整个非线性系统中受到界定。另一方面，对峰值周期波的扰动在$ w^{1，\ infty} $ norm中生长，并可能在有限的时间内在Camassa-Holm方程的非线性演化中爆炸。
Peaked periodic waves in the Camassa-Holm equation are revisited. Linearized evolution equations are derived for perturbations to the peaked periodic waves and linearized instability is proven both in $H^1$ and $W^{1,\infty}$ norms. Dynamics of perturbations in $H^1$ is related to the existence of two conserved quantities and is bounded in the full nonlinear system due to these conserved quantities. On the other hand, perturbations to the peaked periodic wave grow in $W^{1,\infty}$ norm and may blow up in a finite time in the nonlinear evolution of the Camassa-Holm equation.
