Elastic and Inelastic Interaction Behaviours for the (2 + 1)-Dimensional Nizhnik–Novikov

A modified mapping method and new ansätz form are used to derive three families of variable separation solutions with two arbitrary functions of the (2 + 1)-dimensional Nizhnik–Novikov–Veselov equation in water waves. By selecting appropriate functions in the variable separation solution, we discuss interaction behaviours among dromion-pair and dromion-like peakon-pair and dromion-like semifoldon-pair. The analysis results exhibit that the interaction behaviours between dromion-pair and dromion-like peakon-pair, dromion-pair and semifoldon-pair, dromion-like peakon-pair and semifoldon-pair are all incomplete elastic, and there exists a phase shift. The interaction behaviour between two dromion-like semifoldon-pairs is completely elastic, and no phase shift appears after interaction. Moreover, during the interactions between dromion-pair and semifoldon-pair, dromion-like peakon-pair and semifoldon-pair, and between two dromion-like semifoldon-pairs, there all exist a multi-valued semifoldon-pair.