Density-fluctuation symbolic computation on the (3+1)-dimensional variable-coefficient Kudryashov–Sinelshchikov equation for a bubbly liquid with experimental support

Liquids with gas bubbles are commonly seen in medical science, natural science, daily life and engineering. Nonlinear-wave symbolic computation on the (3[Formula: see text]+[Formula: see text]1)-dimensional variable-coefficient Kudryashov–Sinelshchikov model for a bubbly liquid is hereby performed. An auto-Bäcklund transformation and some solitonic solutions are obtained. With respect to the density fluctuation of the bubble-liquid mixture, both the auto-Bäcklund transformation and solitonic solutions depend on the bubble-liquid-viscosity, transverse-perturbation, bubble-liquid-nonlinearity and bubble-liquid-dispersion coefficient functions. We note that some shock waves given by our solutions have been observed by the gas-bubble/liquid-mixture experiments. Effects on a bubbly liquid with respect to the bubble-liquid-viscosity, transverse-perturbation, bubble-liquid-nonlinearity and bubble-liquid-dispersion coefficient functions might be detected by the future gas-bubble/liquid-mixture experiments.