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Stability of Kadomtsev-Petviashvili multi-line solitons

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arxiv 2205.07432 v3 pith:YQTSR4IN submitted 2022-05-16 math.AP nlin.SI

Derchyi Wu This is my paper · ORCID
classification math.APnlin.SI
keywords multi-linescatteringsolitonscontinuousdatakadomtsevpetviashvilistability
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abstract

We prove the long-standing inverse scattering theory (IST) of perturbed Kadomtsev Petviashvili multi-line solitons. Our work is the first rigorous IST of a multi-dimensional integrable system when both continuous and discrete scattering data are present, and the support of continuous scattering data does not degenerate into contours in the complex plane. As an application, an $L^\infty$-stability theorem of the Kadomtsev Petviashvili multi-line solitons is justified.

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Cited by 1 Pith paper

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  1. On the B\"acklund transform and the stability of the line soliton of the KP-II equation on $\mathbb R^2$

    math.AP 2024-12 conditional novelty 8.0 of 10

    A rigorous Bäcklund transform is constructed for KP-II on the plane, and its image is shown to be a codimension-1 manifold, yielding codimension-1 L2 stability of the line soliton at sharp regularity.

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