Stability of periodic waves for the defocusing fractional cubic nonlinear Schrõdinger equation

被引:0
作者
Borluk, Handan [1 ]
Muslu, Gulcin M. [2 ,3 ]
Natali, Fabio [4 ]
机构
[1] Ozyegin Univ, Dept Basic Sci, Istanbul, Turkiye
[2] Istanbul Tech Univ, Dept Math, TR-34469 Maslak, Istanbul, Turkiye
[3] Istanbul Medipol Univ, Sch Engn & Nat Sci, TR-34810 Istanbul, Turkiye
[4] Univ Estadual Maringa, Dept Math, Maringa, PR, Brazil
来源
COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION | 2024年 / 133卷
关键词
Defocusing fractional Schr & otilde; dinger equation; Periodic solutions via constrained; minimization problem; Spectral stability; Newton's iteration method; ORBITAL STABILITY; SOLITARY WAVES; SCHRODINGER;
D O I
10.1016/j.cnsns.2024.107953
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
In this paper, we determine the spectral instability of periodic odd waves for the defocusing fractional cubic nonlinear Schr & otilde;dinger equation. Our approach is based on periodic perturbations that have the same period as the standing wave solution, and we construct real periodic waves by minimizing a suitable constrained problem. The odd solution generates three negative simple eigenvalues for the associated linearized operator, and we obtain all this spectral information by using tools related to the oscillation theorem for fractional Hill operators. Newton's iteration method is presented to generate the odd periodic standing wave solutions and numerical results have been used to apply the spectral stability theory via Krein signature as established in Kapitula et al. (2004) and Kapitula et al. (2005).
引用
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页数:14
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