Reconstruction of multi-soliton interactions using crest data for (2+1)-dimensional KdV type equations

To predict the wave parameters from the interaction patterns of waves (the inverse problem), the corresponding direct problem needs to be solved. In this paper, interaction patterns of multi-soliton solutions of KdV type equations are constructed. The connection between the multi-soliton interaction patterns and the decomposition of a multi-soliton solution into a linear superposition of solitons and interaction solitons is demonstrated. All new concepts are illustrated for three-soliton solutions of the Kadomtshe–Petviashvili equation.