Transverse instability of periodic standing waves for the generalized nonlinear Schrodinger equation

2023/10/05 by Fábio Natali, Natali, Fabio, Gabriel E. Bittencourt Moraes +1
Mathematics · Physics and Astronomy · #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Photonic Systems #Nonlinear Waves and Solitons

paper · pdf · doi:10.48550/arxiv.2310.03467

openalex publication_date 2023/10/05 · openalex created_date 2023/10/09 · openalex updated_date 2026/08/01

Abstract

In this paper, we determine the transverse instability of periodic standing wave solutions for the generalized Schrödinger equation with fractional power nonlinearity. The existence of periodic waves is determined by using a constrained minimization problem in the complex setting, and it is shown that the corresponding real solution, depending on the power nonlinearity, is always positive or changes its sign. The transverse instability results are then determined by applying the main result given in \citeRoussetTzvetkov for the periodic case.

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