Fission, fusion and annihilation in the interaction of localized structures for the (2 + 1)-dimensional generalized Broer–Kaup system

Based on the WTC truncation method and the general variable separation approach (GVSA), we have first found a general solution including three arbitrary functions for the (2 + 1)-dimensional simplified generalized Broer–Kaup (GBK) system (B = 0). A class of double periodic wave solutions is obtained by selecting these arbitrary functions appropriately. The interaction properties of the periodic waves are numerically studied and found to be non-elastic. Limit cases are considered and some new localized coherent structures are obtained, the interaction properties of these solutions reveal that some of them are completely elastic and some are non-completely elastic. After that, starting from the (2 + 1)-dimensional GBK system (B ≠ 0) and using the variable separation approach (VSA) including two arbitrary functions in the general solution, we have constructed by selecting the two arbitrary functions appropriately a rich variety of new coherent structures. The interaction properties of these structures reveal new physical properties like fusion, fission, or both and present mutual annihilation of these solutions as time increasing. The annihilation in this model has found to be rule by the parameter K1, when this parameter is taken to be zero, the annihilation disappears in this model and the above mentioned structures recover the solitonic structure properties.