Center stable manifolds around line solitary waves of the Zakharov--Kuznetsov equation with critical speed

Abstract

In this paper, we construct center stable manifolds around unstable line solitary waves of the Zakharov--Kuznetsov equation on two dimensional cylindrical spaces with $2\pi L$ 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.

arXiv commentarXiv admin note: text overlap with arXiv:1808.07315

References in corpus (5)

• Symmetry-breaking bifurcation in the nonlinear Schrödinger equation with symmetric potentials
• Asymptotic Stability of high-dimensional Zakharov-Kuznetsov solitons
• Stability and instability of the KdV solitary wave under the KP-I flow
• Global Well-posedness for the Cauchy problem of the Zakharov-Kuznetsov equation in 2D
• Center stable manifolds around line solitary waves of the Zakharov--Kuznetsov equation