Decomposition and linear superposition of the (2+1)-dimensional Caudrey–Dodd–Gibbon–Kotera–Sawada equation

Generally, the principle of linear superposition is not applicable in nonlinear systems. The results of our researches prove that for some certain types of decomposed solutions of (2+1)-dimensional Caudrey–Dodd–Gibbon–Kotera–Sawada(CDGKS) equation, the linear superposition principle holds. First, beginning with the potential (2+1)-dimensional CDGKS equation, six sets of decomposition equations are formulated by the formally variable separation approach. On the basis of these decompositions, the linear superposition solutions are then discussed. More specifically, the combination of two periodic wave solutions, soliton and periodic wave interaction solution and the multi-soliton solution are obtained.