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

Handan Borluk, Gulcin M. Muslu*, Fábio Natali

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

Abstract

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 Kapitula et al. (2004) and Kapitula et al. (2005).

Original languageEnglish
Article number107953
JournalCommunications in Nonlinear Science and Numerical Simulation
Volume133
DOIs
Publication statusPublished - Jun 2024

Bibliographical note

Publisher Copyright:
© 2024 Elsevier B.V.

Keywords

  • Defocusing fractional Schrödinger equation
  • Newton's iteration method
  • Periodic solutions via constrained minimization problem
  • Spectral stability

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