2023/10/12 by Handan Borluk, Gülçin M. Muslu, Borluk, Handan +3
Mathematics · #35B10 #35B35 #35Q55 #35R11 #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Fractional Differential Equations Solutions #Numerical methods for differential equations
paper · pdf · doi:10.48550/arxiv.2310.08059
openalex publication_date 2023/10/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper, we determine the spectral instability of periodic odd waves for the defocusing fractional cubic nonlinear Schrödinger 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 [22] and [23].