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.
Stability of Kadomtsev-Petviashvili multi-line solitons
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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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2024 1verdicts
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On the B\"acklund transform and the stability of the line soliton of the KP-II equation on $\mathbb R^2$
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.