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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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.