LAUSR

In this paper, we investigated various exact solutions of (3+1)-dimensional Kudryashov-Sinelshchikov equation in a mixture of liquid and gas bubbles. At first, the linear superposition principle was introduced to obtain resonant multi-soliton solutions and we took two cases as examples to illustrate the wave trajectories and the structure of resonant multi-soliton solutions through several sets of graphs. Next, multiple rogue wave solutions were derived via using the ‘4-2-4’ neural network model and we obtained its 1-rogue wave, 3-rogue wave and 6-rogue wave solutions through symbolic computation. In addition, three-dimensional, contour and density plots of multiple rogue wave solutions vividly shown their physical structure and dynamic properties. Furthermore, these solutions have greatly expanded the exact solutions of (3+1)-dimensional Kudryashov-Sinelshchikov equation on the available literature.