Plenty of molecule structures and interaction solutions in liquid–gas bubble dynamical system

Under investigation in this work is an integrable (3+1)-dimensional nonlinear wave equation describing the dynamic of liquid with gas bubble, which is named as Kudryashov–Sinelshchikov equation. Firstly, the N-soliton solutions are explored based on the Hirota bilinear form. By introducing the velocity resonance mechanism to the N-soliton solutions, it is found that the (3+1)-dimensional Kudryashov–Sinelshchikov equation possesses abundant molecule structures including soliton molecules on the (x, y), (y, z) and (z, x) planes, breather-type molecules and diversified semi-rational molecules. Moreover, localized interaction solutions consisting of soliton molecule, the resonant Y-type soliton, breather and lump wave will be constructed. The obtained solutions are useful in the understanding the nonlinear localized waves and provide some new insight to explain the nonlinear phenomena arising from the areas of nonlinear optics, plasma physics and fluid mechanics.