Abstract
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 that addresses both continuous and discrete scattering data, ensuring that the support of the continuous scattering data does not degenerate into contours in the complex plane. As an application, we justify an L ∞ -stability theorem for the Kadomtsev–Petviashvili multi-line solitons.
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