Approximate Peregrine Solitons in Dispersive Nonlinear Wave Equations

2025/07/02 by Guido Schneider, Schneider, Guido, Nils Thorin +1
Mathematics · Physics and Astronomy · #Dispersionless equation #Dynamics (music) #Envelope (radar) #Fractional Differential Equations Solutions #Nonlinear Photonic Systems #Nonlinear Waves and Solitons #Nonlinear system #Rogue wave #Sobolev space #Wave equation #Wave packet

paper · pdf · doi:10.48550/arxiv.2507.01632

published in arXiv (Cornell University) (Cornell University)

openalex publication_date 2025/07/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The purpose of this short note is to explain how the existing results on the validity of the NLS approximation can be extended from Sobolev spaces H^s(ℝ) to the spaces of functions u = v + w where v ∈ H_per^s and w ∈ H^s(ℝ). This allows us to use the Peregrine solution of the NLS equation to find freak or rogue wave dynamics in more complicated systems.

Citations

• Linear instability of breathers for the focusing nonlinear Schrödinger equation
• Modified Energy Functionals and the NLS Approximation

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