Rogue waves on the periodic wave background in the focusing nonlinear Schrodinger equation

2019/05/28 by Jinbing Chen, Chen, Jinbing, Dmitry E. Pelinovsky +3
Mathematics · Physics and Astronomy · #Advanced Mathematical Physics Problems #Dynamical Systems (math.DS) #Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Nonlinear Photonic Systems #Nonlinear Waves and Solitons #Pattern Formation and Solitons (nlin.PS)

paper · pdf · doi:10.48550/arxiv.1905.11638

openalex publication_date 2019/05/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We present exact solutions for rogue waves arising on the background of periodic waves in the focusing nonlinear Schrodinger equation. The exact solutions are obtained by characterizing the Lax spectrum related to the periodic waves and by using the one-fold Darboux transformation. The magnification factor of the rogue waves is computed in the closed analytical form. We relate the rogue wave solutions to the modulation instability of the periodic wave background.

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