Nonlinear superposition of the (2+1)-dimensional generalized Konopelchenko–Dubrovsky–Kaup–Kupershmidt equation

In this work, the (2+1)-dimensional gKDKK equation is the research object. Different from previous studies, this study aims to obtain the nonlinear superposition of the (2+1)-dimensional gKDKK equation by adding new constraints, which leads to new results of its solution states. The non-collision of lump wave with line wave and breather wave is studied. The results show that the two conditions satisfy the requirement that lump wave does not collide with line wave and lump wave does not collide with breather wave. At the same time, the mixed solutions of lump wave, line wave and breather wave are also studied and the same conclusion is obtained. The results of this nonlinear superposition will break the traditional research and further enrich the dynamic behaviors of nonlinear evolution equations.