论文标题
Zakharov的线孤独波周围的中心稳定歧管 - Kuznetsov方程的临界速度
Center stable manifolds around line solitary waves of the Zakharov--Kuznetsov equation with critical speed
论文作者
论文摘要
在本文中，我们围绕Zakharov的不稳定线孤立波 - Kuznetsov方程在二维圆柱空间上构建中心稳定的歧管，并以$2πl$周期为单位。在上一篇论文中，围绕不稳定的线路孤立波周围的中心稳定歧管，没有临界速度$ c = 4n^2/5l^2 $，用于正整数$ n> 1 $。由于临界速度的线性孤立波周围的线性化运算符是退化的，因此我们通过应用Lyapunov函数的第4阶项估算值来证明中心稳定的稳定歧管的稳定性。
In this paper, we construct center stable manifolds around unstable line solitary waves of the Zakharov--Kuznetsov equation on two dimensional cylindrical spaces with $2πL$ period. In the previous paper, center stable manifolds around unstable line solitary waves have been constructed without critical speed $c =4n^2/5L^2$ for positive integer $n>1$. Since the linearized operator around line solitary waves with critical speed is degenerate, we prove the stability condition of the center stable manifold for critical speed by applying to the estimate of 4th order term of a Lyapunov function.
