Variable separation solutions for the (2+1)-dimensional generalized Nizhnik–Novikov–Veselov equation

In this paper, with the variable separation approach and based on the general reduction theory, we successfully obtain the variable separation solutions for the (2+1)-dimensional generalized Nizhnik–Novikov–Veselov (GNNV) equation with the help of an auxiliary equation. Based on the variable separation solution and by selecting appropriate functions, new types of interactions between the multi-valued and the single-valued solitons, such as compacton-like semi-foldon and compacton, peakon-like semi-foldon and peakon, are investigated. Meanwhile, we also discuss the phase shift of these interactions.