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Approximate Peregrine Solitons in Dispersive Nonlinear Wave Equations (2507.01632v1)
Published 2 Jul 2025 in math.AP
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 $Hs(\mathbb{R})$ to the spaces of functions $u = v + w$ where $v \in H_{{per}}s$ and $w \in Hs(\mathbb{R})$. 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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