Finding the interaction solutions to the dimensionally reduced equations based on computerized symbolic computation

Abstract

With symbolic computation, we study two dimensionally reduced nonlinear equations, which are cast into bilinear forms firstly. The interaction solutions between lump and soliton are computed, respectively, for these two equations. Hereby, we assume the solution to the bilinear equation consisting of a sum of two squares functions and a cosh function. With limitation analysis and graphical illustrations, the interaction process is simulated based on the expressions of the interaction solutions. We find the lump interacts with the soliton, and moves from the one hump (e.g. the left or the right hump) of the soliton to the other one (the right or the left hump).