The nonlinear superposition between anomalous scattering of lumps and other waves for KPI equation

Normally, lump waves with different velocities and amplitudes produce different phase shifts when they collide with line or breather waves. Based on the Gram determinant form of the solution, we consider a new hybrid solution consisting of two weakly interacting lump waves and line waves by means of some clever limit tricks for the Kadomtsev–Petviashvili I equation. In this new hybrid solution, each lump wave moves along the curve with a variable velocity, and lump waves have the same velocity and amplitude as | t | tends to infinity. Moreover, it is interesting that anomalous scattered lump waves exhibit the same dynamical properties when they collide with the line wave. The same phenomena also exist in the nonlinear superposition between anomalous scattering of lumps and breather waves.