SOLITON, MULTIPLE-LUMP, AND HYBRID SOLUTIONS FOR A (3+1)-DIMENSIONAL GENERALIZED KONOPELCHENKO-DUBROVSKY-KAUP-KUPERSHMIDT EQUATION IN PLASMA PHYSICS, FLUID MECHANICS, AND OCEAN DYNAMICS

In this paper, we investigate a (3+1)-dimensional generalized Konopelchenko-Dubrovsky-Kaup-Kupershmidt equation in plasma physics, fluid mechanics, and ocean dynamics. Based on the existing bilinear form, we construct the N-soliton solutions, where N is a positive integer. Besides, we obtain the M-lump solutions via the long-wave limit to the N-soliton solutions, where M is a positive integer. Dark one-lump solutions are derived. Moreover, we take M = 2 and M = 3 to derive the two- and three-lump solutions, respectively. We find that the shapes and amplitudes of the dark one-, two-, and three-lump waves remain unchanged during propagation. Finally, three types of hybrid solutions are discussed, namely, the one-lump wave and one-soliton wave, the one-lump wave and two-soliton waves, and the two-lump waves and one-soliton wave.