N-soliton solutions, M-lump wave and physical phenomena between N-soliton solutions and M-lump to some types of partial differential equations

The purpose of this study is to construct N-soliton solutions, fusion solutions, M-lump waves, lump solutions, and the physical collision between N-soliton solutions with lump waves to some partial differential equations via Hirota simple method. First, we convert partial differential equations to a bilinear form via logarithmic variable transform. We use the general form of N-soliton solutions to find the N-soliton solutions to the studied partial differential equations. To study M-lump waves, we use the long-wave limit method, and to investigate Lump solutions we use quadratic function solutions.