In this research work, we investigate the complex structure of soliton in the Fractional
Kudryashov–Sinelshchikov Equation (FKSE) using conformable fractional derivatives. Our study
involves the development of soliton solutions using the modified Extended Direct Algebraic Method
(mEDAM). This approach involves a key variable transformation, which successfully transforms the
model into a Nonlinear Ordinary Differential Equation (NODE). Following that, by using a series
form solution, the NODE is turned into a system of algebraic equations, allowing us to construct
soliton solutions methodically. The FKSE is the governing equation, allowing for heat transmission
and viscosity effects while capturing the behaviour of pressure waves in liquid–gas bubble mixtures.
The solutions we discover include generalised trigonometric, hyperbolic, and rational functions with
kinks, singular kinks, multi-kinks, lumps, shocks, and periodic waves. We depict two-dimensional,
three-dimensional, and contour graphs to aid comprehension. These newly created soliton solutions
have far-reaching ramifications not just in mathematical physics, but also in a wide range of subjects
such as optical fibre research, plasma physics, and a variety of applied sciences. |
