Stability criterion for solitons of the Zakharov–Kuznetsov-type equations
Stability criterion for solitons of the Zakharov–Kuznetsov-type equations
复制标题
Zakharov-Kuznetsov 型方程孤子的稳定性判据
DOI：
10.1016/j.physleta.2018.05.026
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发表时间：
2017
影响因子：
2.6
通讯作者：
E. Kuznetsov
中科院分区：
文献类型：
--
作者：
E. Kuznetsov
关于 KDV 型方程 \cite{KUZNETSOV1984314} 中孤子线性稳定性的早期结果被推广到由 ZK 型方程描述的孤子。对于具有任意非线性的方程，推导了 Vakhitov-Kolokolov 形式的地孤子的线性稳定性判据。对于幂非线性，不稳定准则与下面的哈密顿无界性条件一致。后者代表了此类系统中出现崩溃的主要特征。
Early results concerning the linear stability of the solitons in equation of the KDV-type \cite{KUZNETSOV1984314} are generalized to solitons describing by the ZK-type equation. The linear stability criterion for ground solitons in the Vakhitov-Kolokolov form is derived for such equations with arbitrary nonlinearity. For the power nonlinearity the instability criterion coincides with the condition of the Hamiltonian unboundedness from below. The latter represents the main feature for appearance of collapse in such systems.