Jisha, J.Dubey, R.K.Benton, D.Rashid, A.2026-02-042022Physica Scripta, 2022, 97, 9, pp. -318949https://doi.org/10.1088/1402-4896/ac89bahttps://idr.nitk.ac.in/handle/123456789/22416The Kudryashov and Sinelshchikov (KS) equation address pressure waves in liquid-gas bubble mixtures while considering heat transport and viscosity. This study mainly includes two types of generalized solutions: polynomial function traveling wave solutions and rational function traveling wave solutions. In this study, we constructed the KS equation's exact traveling and solitary wave solutions with variable coefficients by the generalized unified method (GUM). These newly created solutions play a significant role in mathematical physics, optical fiber physics, plasma physics, and other applied science disciplines. We illustrated the dynamical behavior of the discovered solutions in three dimensions. We proposed the possibility of discussing wave interaction and other wave structures using bilinear form related to the Hirota method for the fractional solutions. © 2022 IOP Publishing Ltd.Korteweg-de Vries equationLiquefied gasesOptical fibersPolynomialsSolitonsExact solutionKorteweg-de Vries-equationMulti-rational solutionPressure wavesRational solutionThe generalized unified methodTraveling wave solutionUnified methodVariable coefficientsRational functions