Soliton molecule and their interaction solutions for the (2 + 1)-dimensional gKDKK equation

The [Formula: see text]-soliton solution of the [Formula: see text]-dimensional generalized Konopelchenko–Dubrovsky–Kaup–Kupershmidt (gKDKK) equation is constructed through taking the Bäcklund transformation, the Hirota bilinear method and the auxiliary function [Formula: see text], which is combined by several elementary functions. The line soliton molecule, lump and breather solutions are first presented. The explicit expressions of the soliton molecules, including the line soliton mixed with breather/lump, can also be constructed. The interaction solutions among soliton molecule, lump and breather structures are finally achieved. These results mainly introduce the ideas of velocity resonance, module resonance of wavenumber and long-wave limit. In order to illustrate these phenomena, the analytical solutions are shown and the dynamical features are depicted through the Maple software.