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In this paper, we studied a novel form of exact analytical solutions of (2+1)-dimensional Ito equation based on Hirota bilinear method. By using symbolic computation, assorted exact analytical solutions including high-order rational solutions, three-wave solutions, breather solutions and interaction solutions between the above solutions were obtained through choosing the order of terms as well as different basic functions. The exact solutions of (2+1)-dimensional Ito equation on current literatures are extremely enriched. Furthermore, both three-dimensional plots and corresponding contour maps with different determinant values vividly show the movement of waves and the collision phenomena.

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.

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