Rational Solutions to the KPI Equation as Multi-lumps with a One Degree of Summation

In this paper, we construct solutions to the Kadomtsev–Petviashvili equation (KPI) by using a Darboux transformation with particular genera-ting functions limited to one degree of summation. With this choice, we get rational solutions expressed in terms of a wronskian of order N depending on \(N(D+5)\) $N(D+5)$ real parameters. In this case, we construct explicitly multi-parametric rational solutions to the KPI equation and we study the patterns of their modulus in the plane (x, y) and their evolution according to time and parameters.