The inverse scattering theory of Kadomtsev-Petviashvili II equations

An overview of the inverse scattering theory of the Kadomtsev Petviashvili II equation with an emphasis on the inverse problem for perturbed KP multi line solitons is provided. It is shown that, despite additional algebraic or analytic techniques are introduced due to new singular structures, there exists a consistency of the inverse scattering theories for different backgrounds such as the vacuum, $1$-line solitons, and multi line solitons.