The phase transition of control parameters for the (3+1)-dimensional Konopelchenko–Dubrovsky–Kaup–Kupershmidt equation in plasma or ocean dynamics

The study of nonlinear waves is a significant topic in the field of fluid Physics. In this paper, we study the nonlinear transformed waves, interactions and transformed molecular waves of the (3+1)-dimensional Konopelchenko-Dubrovsky-Kaup-Kupershmidt equation in plasma or ocean dynamics. Based on the condition of state transition, the transformed wave solutions derived from breath waves are obtained. The dynamics of the transformed wave solutions change with time, including peaks and shapes. In addition, we report two kinds of interactions, namely long- and short-lived collisions. The long-lived collision mode reveals the two constituent elements are always intertwined with each other. However, there is only disposable collision in short-lived collision mode, which is also considered as a catch-up case. As special interactions, the transformed molecular waves considered as a collision free mode whose atoms are transformed waves are investigated. The breather-breather molecule, breather-M-shaped molecule and double M-shaped molecule via velocity resonance condition are given. In summary, graphical investigations indicate that the novel transformed wave structures are shown for application in fluid mechanics.