Optical solitons for the Kudryashov–Sinelshchikov equation by two analytic approaches

This paper employs two ansatz-based methods to investigate a wide array of analytical soliton solutions within the framework of the Kudryashov–Sinelshchikov (KS) equation. This equation accounts for thermal expansion and viscosity effects, illustrating the emergence of pressure waves in mixtures containing liquid gas bubbles. The study utilizes the Sardar Subequation (SSE) technique and the Jacobi elliptic function (JEF) technique to derive analytical soliton solutions manifest as trigonometric, hyperbolic, rational, and exponential functions. These solitons encompass diverse characteristics, including singletons, mixed dark-singular solitons, combined dark-bright solitons, single and bright solitons, shock waves, solitary waves, and periodic and double periodic solitons. By appropriately selecting parameter values, the research illustrates two-dimensional and three-dimensional graphical representations of specific solutions, enhancing the study’s credibility. The derived analytical wave solutions underscore the effectiveness and reliability of the SSE and JEF techniques in analyzing the KS equation’s soliton behavior.