论文标题
关于阻尼高阶非线性schrödinger方程的呼吸型溶液的稳定
On the stabilization of breather-type solutions of the damped higher order nonlinear Schrödinger equation
论文作者
论文摘要
非线性Schrö\ -Dinger（NLS）方程的空间周期性呼吸溶液（SPB）经常用于模拟流氓波，通常是不稳定的。在本文中，我们研究了耗散和高阶非线性对在阻尼高阶NLS（HONLS）方程的框架中单模SPB稳定的影响。我们观察到与临界状态的发展相关的新型不稳定性的发作，这是由于阻尼HONLS系统中对称性破坏而产生的。我们使用NLS的偶数溶液来扩大NLS方程解的不稳定性的浮雕表征，以表明不稳定性与周期性和连续floquet Spectrum的退化复杂元素有关。结果，在消除频谱的所有复杂变性元件围绕消除的honls中心稳定溶液的浮标标准。对于具有给定模式结构的初始SPB，扰动分析表明，仅在短时间内，与在阻尼的Honl下分裂的复合双点相关的复杂双点，而与非谐波模式相关的谐音则保持有效关闭。相应的抑制HONL数值实验证实了与非谐波模式相关的不稳定性比与共振模式相关的不稳定性持续更长的时间尺度。
Spatially periodic breather solutions (SPBs) of the nonlinear Schrö\-dinger (NLS) equation are frequently used to model rogue waves and are typically unstable. In this paper we study the effects of dissipation and higher order nonlinearities on the stabilization of both single and multi-mode SPBs in the framework of a damped higher order NLS (HONLS) equation. We observe the onset of novel instabilities associated with the development of critical states which result from symmetry breaking in the damped HONLS system. We broaden the Floquet characterization of instabilities of solutions of the NLS equation, using an even 3-phase solution of the NLS as an example, to show instabilities are associated with degenerate complex elements of both the periodic and continuous Floquet spectrum. As a result the Floquet criteria for the stabilization of a solution of the damped HONLS centers around the elimination of all complex degenerate elements of the spectrum. For an initial SPB with a given mode structure, a perturbation analysis shows that for short time only the complex double points associated with resonant modes split under the damped HONLS while those associated with nonresonant modes remain effectively closed. The corresponding damped HONLS numerical experiments corroborate that instabilities associated with nonresonant modes persist on a longer time scale than the instabilities associated with resonant modes.
