Lump interactions and collapse in the modified Zakharov-Kuznetsov equation

Two-dimensional solitary wave (lump) interactions and the formation of sing ularities in the modified Zakharov-Kuznetsov (mZK) equation are considered. The mZK equation represents an anisotropic two-dimensional generalization of the Korteweg-deVries equation and can be derived in a magnetized plasma for small amplitude Alfven waves at a critical angle to the undisturbed mag netic field. The radially symmetric positive solutions (lumps) for the mZK equation are computed. It is shown that when two lumps interact, the initia l energy exchange between them is followed by the emergence of a single col lapsing lump and a radiation field behind it, Connections to the analytic t heory of collapse for the mZK equation are discussed.