Lump solitons and the interaction phenomena of them for two classes of nonlinear evolution equations

Lump solitons are obtained from (2+1)-dimensional Ito equation and (2+1)-dimensional CDGKS equation by using a direct method and the completely non-elastic interaction between a lump and a stripe of (2+1)-dimensional Ito equation is presented, which shows a lump soliton is drowned or swallowed by a stripe soliton. The direct method is based on Hirota bilinear form of the equations that have special solutions of quadratic function. The general formula of coordinates of the vertex and the amplitude of lump solitons are given. The dynamical character shows in this work enriches the variety of the dynamics of higher dimensional nonlinear wave field.