On the Inverse Scattering Transform for the Kadomtsev‐Petviashvili Equation

The initial value problem of the Kadomtsev‐Petviashvili equation for one choice of sign in the equation has been recently investigated in the literature. Here we consider the other choice of sign. We introduce suitable eigenfunctions which though bounded are not analytic in the spectral parameter. This, in contrast to the known case, prevents us from formulating the inverse problem as a nonlocal Riemann‐Hilbert boundary value problem. Nevertheless a suitable formulation is given and a formal solution is constructed via a linear integral equation.