Explicit Solutions to the (3+1)-Dimensional Kudryashov-Sinelshchikov Equations in Bubbly Flow Dynamics

Abstract

A modified tanh-coth method with Riccati equation is used to construct several explicit solutions of (3+1)-dimensional Kudryashov-Sinelshchikov equations in bubble gas liquid flow. The solutions include solitons and periodic solutions. The method applied can be used in further works to obtain entirely new solutions to many other nonlinear evolution equations.

Novel Insights into the Exact Solutions of the Modified (3+1) Dimensional Fractional KS Equation with Variable Coefficients

“…For visualizing the dynamical behavior of the solution (21), we consider the particular values to arbitrary functions and arbitrary constants:…”

“…Their research likely explores the analytical properties, solution techniques, and implications of the KS equation, contributing to understanding nonlinear wave phenomena in fluid dynamics. The (3+1)-dimensional variable coefficient Kudryashov and Sinelshchikov (vcKS) equation with regular time derivative model solved using Hirota's bilinear and other methods are discussed in [20][21][22][23][24][25]. In the context of plasmas, the KS equation provides a mathematical framework to investigate the dynamics of ion-acoustic solitons.…”