Generalized variational structures of the (3+1)-dimensional Zakharov–Kuznetsov–Burgers equation in dusty plasma

The center of this paper is to establish the generalized variational structure (GVS) of the Formula: see text-dimensional Zakharov–Kuznetsov–Burgers equation (ZKBe) by taking advantage of the Semi-inverse method (SIM). Two different GVSs are extracted and the derivation process is presented in detail. The extracted GVSs reveal the energy conservation law and can offer some new insights on the study of the variational method.