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arXiv · 2507.01632

Approximate Peregrine Solitons in Dispersive Nonlinear Wave Equations

Guido Schneider·Nils Thorin
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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 $H^s(\mathbb{R})$ to the spaces of functions $u = v + w$ where $v \in H_{{per}}^s$ and $w \in H^s(\mathbb{R})$. This allows us to use the Peregrine solution of the NLS equation to find freak or rogue wave dynamics in more complicated systems.

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Guido Schneider, Nils Thorin. 2025-07-02. Approximate Peregrine Solitons in Dispersive Nonlinear Wave Equations. https://arxiv.org/abs/2507.01632

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