Rich Localized Coherent Structures of the (2 + 1)-Dimensional Broer–Kaup–Kupershmidt Equation**The project supported by the National Outstanding Youth Foundation of China (No. 19925522), the Research Fund for the Doctoral Program of High Education of China (No. 2000024832), the National Natural Science Foundation of Zhejian Province of China (No. 102053) and the Foundation of Zhejian Normal University (No. 20021068).

Abstract

Using a Bäcklund transformation and the variable separation approach, we find there exist abundant localized coherent structures for the (2 + 1)-dimensional Broer–Kaup–Kupershmidt (BKK) system. The abundance of the localized structures for the model is introduced by the entrance of an arbitrary function of the seed solution. For some special selections of the arbitrary function, it is shown that the localized structures of the BKK equation may be dromions, lumps, ring solitons, peakons, or fractal solitons etc.