Narrow Results

With the help of a mapping approach, a new type of variable separation solution with two arbitrary functions to (2+1)-dimensional Boiti–Leon–Pempinelli system (BLP) is derived. Based on the derived variable separation solution, some single valued and multiple valued localized excitations such as dromions, peakons and foldons, etc. with novel evolutional properties are revealed by introducing appropriate initial conditions in this paper.

Using an extended mapping approach and a special Painlevé–Bäcklund transformation, respectively, we obtain two families of exact solutions to the (2+1)-dimensional Boiti–Leon–Martina–Pempinelli (BLMP) system. In terms of the derived exact solution, we reveal some novel evolutional behaviors of localized excitations, i.e., fission, fusion, and annihilation phenomena in the (2+1)-dimensional BLMP system.