Instability of the solitary waves for the generalized derivative nonlinear Schrödinger equation in the degenerate case
Instability of the solitary waves for the generalized derivative nonlinear Schrödinger equation in the degenerate case
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DOI：
10.1016/j.jde.2023.02.061
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发表时间：
2018-03
影响因子：
2.4
通讯作者：
C. Miao;Xingdong Tang;Guixiang Xu
中科院分区：
文献类型：
--
作者：
C. Miao;Xingdong Tang;Guixiang Xu
In this paper, we make use of the modulation analysis, the perturbation argument and the Virial type identity in the radiation term similar as those in [17] to show the orbital instability of the solitary waves Q ω, c (x− c t) e i ω t of the generalized derivative nonlinear Schrödinger equation (gDNLS) in the degenerate case c= 2 z 0 ω, where z 0= z 0 (σ) is the unique zero point of F (z; σ) in (− 1, 1). The new ingredients in the proof are the refined modulation decomposition of the solution near Q ω, c according to the Hamiltonian structure of (gDNLS) and the refined construction of the Virial type identity in the degenerate case. Our argument is qualitative, and we improve the result in [6].
