Pattern Formation of a Bubbly Fluid Mixture under the Effect of Thermodynamics via Kudryashov-Sinelshchikov Model

In this paper, new explicit wave solutions via liquid-gas bubbles are obtained for the fractional Kudryashov-Sinelshchikov (KS) equation under thermodynamic assumptions. A definition is applied to get these that utilized represent phenomenon of pressure waves conditions. Two analytical techniques used explore model which sinh-Gorden expansion and Riccati-Bernoulli Sub-ODE methods. These approaches provide complex hyperbolic, trigonometric, trigonometric KS equation, particularly singular, combined dark, bright, dark-bright, other soliton solutions. Furthermore, acquired results illustrated by 3D graphs suitable parametric values highlight physical importance dynamical behaviors equation. It also demonstrated purposed powerful strategies developing exact traveling a wide range problems found in mathematical sciences.