论文标题
B-Camassa-Holm方程中平滑孤波的稳定性
Stability of smooth solitary waves in the b-Camassa-Holm equation
论文作者
论文摘要
我们得出了在Camassa-Holm方程的B家族中平滑孤立波的精确稳定性标准。光滑的孤立波在恒定背景下存在。在可集成的情况B = 2和B = 3中，我们通过分析表明，稳定性标准是满足的，而平滑的单个波则相对于$ H^3（\ Mathbb {r}）$的扰动轨道稳定。在不可综合的情况下，我们在数值和渐近上表明，每个b> 1满足稳定性标准。与可在可集成的情况中可用的汉密尔顿公式相比，轨道稳定性理论依赖于不同的汉密尔顿公式。
We derive the precise stability criterion for smooth solitary waves in the b-family of Camassa-Holm equations. The smooth solitary waves exist on the constant background. In the integrable cases b = 2 and b = 3, we show analytically that the stability criterion is satisfied and smooth solitary waves are orbitally stable with respect to perturbations in $H^3(\mathbb{R})$. In the non-integrable cases, we show numerically and asymptotically that the stability criterion is satisfied for every b > 1. The orbital stability theory relies on a different Hamiltonian formulation compared to the Hamiltonian formulations available in the integrable cases.
