Study on dynamical behavior of multiple lump solutions and interaction between solitons and lump wave

In this paper, a new (3+1)-dimensional Hirota bilinear equation in fluids is investigated. The interaction solutions of lump and N-soliton ( $$N>1$$ ) are obtained. When $$N=2, 3, 4$$ , new dynamical behavior is analyzed. The interaction of lump and periodic solutions is studied, including lump and 1-periodic solution and lump and 2-periodic solution. The interaction of lump, periodic and 1-soliton solutions is discussed. Finally, we obtain the multi-lump solutions, including 1-order, 2-order and 3-order lump solutions.