Bilinear forms, N-soliton solutions, breathers and lumps for a (2+1)-dimensional generalized breaking soliton system

In this paper, a ([Formula: see text])-dimensional generalized breaking soliton system, for the interactions of the Riemann wave with a long wave, is investigated. Via the Hirota method, bilinear forms different from those in the existing literatures are derived. [Formula: see text]-soliton solutions are constructed via the Wronskian technique. Solitons with the crest curves being curvilineal are constructed, whose shape changes with the propagation. Parallel solitons have been obtained. Directions of the soliton propagation change, and speeds of the solitons are different: The higher the amplitude of the soliton is, the faster the soliton propagates. Breathers are constructed. Solutions consisting of a lump and two solitons are derived: Two solitons propagate in the same direction and the lump occurs in the region of the interaction between the two solitons.