Asymptotic analysis of multilump solutions of the Kadomtsev–Petviashvili-I equation

We construct lump solutions of the Kadomtsev–Petviashvili-I equation using Grammian determinants in the spirit of the works by Ohta and Yang. We show that the peak locations depend on the real roots of the Wronskian of the orthogonal polynomials for the asymptotic behaviors in some particular cases. We also prove that if the time goes to $-\infty$, then all the peak locations are on a vertical line, while if the time goes to $\infty$, then they are all on a horizontal line, i.e., a $\pi/2$ rotation is observed after interaction.