Exploring Propagating Soliton Solutions for the Fractional Kudryashov–Sinelshchikov Equation in a Mixture of Liquid–Gas Bubbles under the Consideration of Heat Transfer and Viscosity

Abstract

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.

Study of traveling soliton and fronts phenomena in fractional Kolmogorov-Petrovskii-Piskunov equation

“…The global occurrence of nonlinearity underlines the need of constructing nonlinear models, particularly those incorporating Partial Differential equations (PDEs) and Fractional PDEs (FPDEs) [1][2][3][4]. Many researchers have been drawn to investigating nonlinear FPDEs because of their numerous applications in chemistry, acoustics, fluid dynamics, image processing, biology, physics, vibration, and control [5][6][7].…”

Exploring chaotic behavior of optical solitons in complex structured Conformable Perturbed Radhakrishnan-Kundu-Lakshmanan Model

“…Comprehensive understanding of system conduct is made possible by analytical solutions, which also make it easier to do additional theoretical research and inspect the physical influences. In order to address FPDEs, several analytical techniques have been established, including the Variational Iteration Method [10], the fractional differential transform method [11], the ¢ G G ( )-expansion technique [12], the Exp-function approach [13], the tan-expansion approach [14], the Adomian decomposition method [15], the Laplace transform method [16] and the extended direct algebraic method [17,18] and many others [19][20][21][22][23][24][25][26][27][28][29].…”

Diverse soliton solutions to the nonlinear partial differential equations related to electrical transmission line

“…Reference [26] utilized the general extended direct algebraic method to explore the dynamics of the fractional Schrödinger equation, showcasing various families of periodic soliton solutions and their complex interrelationships. Additionally, the modified Extended Direct Algebraic Method has been applied to examine the existence and dynamics of solitary wave solutions in the context of fractional quantum mechanics equations [27], the Kudryashov-Sinelshchikov equation [28], and the coupled Higgs system [29].…”